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Theorem spimv 1943
Description: A version of spim 1928 with a distinct variable requirement instead of a bound variable hypothesis. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
spimv.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spimv  |-  ( A. x ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem spimv
StepHypRef Expression
1 nfv 1609 . 2  |-  F/ x ps
2 spimv.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spim 1928 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem is referenced by:  aev  1944  spv  1951  ax16i  1999  aev-o  2134  reu6  2967  el  4208  ax10ext  27708
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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