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Theorem spimev 1784
Description: Distinct-variable version of spime 1671. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
spimev.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spimev  |-  ( ph  ->  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hints:    ph( y)    ps( x, y)

Proof of Theorem spimev
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
2 spimev.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spime 1671 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391
This theorem is referenced by:  speiv  1785  rnxpid  4817
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