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Yes! And who was that referring to in the above scriptures you cited, Mat 3:11 and Acts 1:5? The apostles.
Read the words of John the Baptist in Luke 3:16, and Jesus words to his apostles in Luke 24:49, then the words of Peter in Acts 1:4-5, then Acts 2:1-4, then Acts 2:16-17.
And then...