There are several reasons as to why we can know that Cornelius and his household were not baptized in the Holy Spirit.
Baptism in the Holy Spirit is discussed in Matthew 3:11, Mark 1:8, Luke 3:16, John 1:33, Acts 1:4-5, and 11:16. It is the same gift equivalent to the gift of apostleship that was given to thirteen apostles in Acts 2:1-4 and by implication upon Paul in Acts 9.
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