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Theorem spimv 1930
Description: A version of spim 1915 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 1605 . 2  |-  F/ x ps
2 spimv.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spim 1915 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  aev  1931  spv  1938  ax16i  1986  aev-o  2121  reu6  2954  el  4192  ax10ext  27606
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
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