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Theorem spimv 1963
Description: A version of spim 1957 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 1629 . 2  |-  F/ x ps
2 spimv.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spim 1957 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549
This theorem is referenced by:  spv  1965  aev  2047  ax16i  2130  aev-o  2258  reu6  3115  el  4373  ax10ext  27574
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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