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Theorem spimv 1961
Description: A version of spim 1955 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 1626 . 2  |-  F/ x ps
2 spimv.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spim 1955 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546
This theorem is referenced by:  spv  1963  aev  2011  ax16i  2095  aev-o  2232  reu6  3083  el  4341  ax10ext  27474
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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