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Theorem a5i 1476
Description: Inference generalizing a consequent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
a5i.1  |-  ( A. x ph  ->  ps )
Assertion
Ref Expression
a5i  |-  ( A. x ph  ->  A. x ps )

Proof of Theorem a5i
StepHypRef Expression
1 hba1 1474 . . 3  |-  ( A. x ph  ->  A. x A. x ph )
2 ax-5 1377 . . 3  |-  ( A. x ( A. x ph  ->  ps )  -> 
( A. x A. x ph  ->  A. x ps ) )
31, 2syl5 32 . 2  |-  ( A. x ( A. x ph  ->  ps )  -> 
( A. x ph  ->  A. x ps )
)
4 a5i.1 . 2  |-  ( A. x ph  ->  ps )
53, 4mpg 1381 1  |-  ( A. x ph  ->  A. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1377  ax-gen 1379  ax-ial 1468
This theorem is referenced by:  hbae  1648  equveli  1684  hbsb2a  1729  hbsb2e  1730  aev  1735  dveeq2or  1739  hbsb2  1759  nfsb2or  1760  reu6  2790
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