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Theorem a5i 1507
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 1505 . . 3  |-  ( A. x ph  ->  A. x A. x ph )
2 ax-5 1408 . . 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 1412 1  |-  ( A. x ph  ->  A. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1408  ax-gen 1410  ax-ial 1499
This theorem is referenced by:  hbae  1681  equveli  1717  hbsb2a  1762  hbsb2e  1763  aev  1768  dveeq2or  1772  hbsb2  1792  nfsb2or  1793  reu6  2846
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