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Theorem a5i 1417
Description: Inference generalizing a consequent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
a5i.1 (xφψ)
Assertion
Ref Expression
a5i (xφxψ)

Proof of Theorem a5i
StepHypRef Expression
1 hba1 1415 . . 3 (xφxxφ)
2 ax-5 1316 . . 3 (x(xφψ) → (xxφxψ))
31, 2syl5 28 . 2 (x(xφψ) → (xφxψ))
4 a5i.1 . 2 (xφψ)
53, 4mpg 1320 1 (xφxψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1226
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1316  ax-gen 1318  ax-ial 1409
This theorem is referenced by:  hbae  1588  equveli  1624  hbsb2a  1669  hbsb2e  1670  aev  1675  dveeq2or  1679  hbsb2  1699  nfsb2or  1700  reu6  2707
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