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Theorem bj-spimevv 31369
Description: Version of spimev 2114 with a dv condition, which does not require ax-13 2102. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-spimevv.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-spimevv  |-  ( ph  ->  E. x ps )
Distinct variable groups:    x, y    ph, x
Allowed substitution hints:    ph( y)    ps( x, y)

Proof of Theorem bj-spimevv
StepHypRef Expression
1 nfv 1772 . 2  |-  F/ x ph
2 bj-spimevv.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2bj-spimev 31367 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1674
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-12 1944
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1458  df-ex 1675  df-nf 1679
This theorem is referenced by:  bj-axsep  31454  bj-dtru  31458
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