Acts 11:13

And he told us how he had seen the angel standing in his house, and saying, Send to Joppa, and fetch Simon, whose surname is Peter; who shall speak unto thee words, whereby thou shalt be saved, thou and all thy house.

Words whereby thou shalt be saved ... Implicit in this is the fact that the baptism of the Holy Spirit was not in order to save Cornelius, nor were all of the alms-giving and prayers sufficient to save him. As Bruce expressed it, "Salvation did not enter Cornelius' house until Peter came there with the gospel."[11] A necessary deduction from this is that Cornelius' baptism was a prior condition of his being saved, the command that he should be baptized being, in fact, the only commandment Peter addressed to him.

Johnson declared that "This is the first instance of a household baptism named in Acts."[12] Who are meant by this "household" are "his kinsmen and near friends" (Acts 10:24), there being no mention of infants. It is declared that these who were baptized in the Holy Spirit and commanded to be baptized in water "heard" the gospel (Acts 10:45).

[11] F. F. Bruce, op. cit., p. 235.

[12] B. W. Johnson, The New Testament with Explanatory Notes (Delight, Arkansas: Gospel Light Publishing Company), p. 464.