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Theorem spimev 1834
Description: Distinct-variable version of spime 1720. (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 1509 . 2  |-  F/ x ph
2 spimev.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spime 1720 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438
This theorem is referenced by:  speiv  1835  rnxpid  4981
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