The proof is in what the Holy Spirit did in both cases.
Yes, they do. But as you so kindly pointed out, they two have the events in reverse order.
In Acts 10 the Holy Spirit comes in power, just as He did on Pentecost. But as demonstrated in John 20:22, the indwelling of the Holy Spirit had already been received by the disciples,
Not so.
John 20:22
And when he had said this, he breathed on them and said to them, Receive the Holy Spirit.
When the Lord Jesus said, "Receive the Holy Spirit" (John 20:22) it is to be understood prophetically to what took place in Acts 2:4 because:
a. Thomas wasn’t there when this event took place, but he was there with the others during Pentecost.
b. According to Luke 24:49 the Lord Jesus stated "I
am sending" the Holy Spirit to them, whereas the second half of the passage points to this taking place at a later date.
Luke 24:49
And behold, I am sending the promise of my Father upon you.
But stay in the city until you are clothed with power from on high.
W. E. Vine asserts that what is described in John 20:22 "was symbolic of the Holy Spirit about to be sent in the world, and with the effect of their ministry of the gospel in the forgiveness of sins by the Spirit's power, or the retention of sins by the rejection of the message (vv. 23, 24). It was a prophetic act as well as symbolic" (John: His Record of Christ, page 183).
Wayne Grudem concurs: When Jesus breathed on his disciples and said to them, "Receive the Holy Spirit" (John 20:22), it probably was an acted-out prophecy about what would happen to them at Pentecost. In the same context - in fact, in the verse immediately preceding - Jesus had told them something that would not happen until Pentecost: "As the Father has sent me, even so I send you" (John 20:21). But even though he said this before he had ascended into heaven, he did not really send them out to preach the gospel until the Day of Pentecost had come. Therefore, his words were looking forward to what would happen a Pentecost. It is best to understand the words in the next sentence, "Receive the Holy Spirit," in the same way - he was speaking in advance of something that would happen on the Day of Pentecost. On that day they would receive the new covenant fullness and power of the Holy Spirit, a much greater empowering of the Holy Spirit than what they had experienced before (Systematic Theology: An Introduction to Biblical Doctrine, page 769, footnote 13).
The indwelling, as pointed out in Acts 2:38, is the result of baptism, which Cornelius had not received yet.
He didn't yet receive water baptism, but he already had the indwelling of the Holy Spirit.
To receive the gift of the Holy Spirit is to receive the indwelling of the Holy Spirit.
Correct. This is not asserted in Acts 10. It is stated in Acts 2:38.
There is an equality of events between the Holy Spirit coming in fire in Acts 2:4 and in Acts 10. But these are not the same as promised in Acts 2:38.
The gift of the Holy Spirit is the Holy Spirit in Acts 2:38 and Acts 10:45
1. The same phrase
2. By the same author
3. In the same book
4. In the same context (the preaching of the gospel which includes the Lordship and resurrection of Christ; cf. Acts 2:21, 23-24; 10:36, 39-40)
1. BDAG (3rd Edition): receive the Spirit as a gift Ac. 2:38; cp. 10:45 (dōrea, page 266).
2. Exegetical Dictionary of the New Testament (EDNT): The usage of dōrea in the NT is concentrated on the gracious gift which has already been given by God, namely, Christ (John 4:10), the Spirit (Acts 2:38; 8:20; 10:45; 11:17), or "righteousness" (Rom. 5:15, 17) (1:364, dōrea, G. Schneider).
3. Theological Dictionary of the New Testament (TDNT): In Ac. the Spirit is called the dōrea of God in 2:38; 8:20; 10:45; 11:17 (2:167, dōrea, Buchsel).
4. Thayer's Greek-English Lexicon of the New Testament: with an epexegetical gen. of the thing given, the Holy Ghost, Ac 2:38, 10:45 (dōrea, page 161).
These Gentiles were given the Holy Spirit as a guarantee.
Acts 15:8
giving them the Holy Spirit
2 Corinthians 5:5
He who has prepared us for this very thing is
God, who has given us the Spirit as a guarantee.
1. Theological Dictionary of the New Testament (TDNT):
The Spirit whom God has given them is for Christians the guarantee of their full possession of salvation (1:475, arrabōn, Behm).