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Theorem bj-spimevw 31313
Description: Existential introduction, using implicit substitution. This is to spimeh 1851 what spimvw 1853 is to spimw 1852. (Contributed by BJ, 17-Mar-2020.)
Hypothesis
Ref Expression
bj-spimevw.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-spimevw  |-  ( ph  ->  E. x ps )
Distinct variable groups:    x, y    ph, x
Allowed substitution hints:    ph( y)    ps( x, y)

Proof of Theorem bj-spimevw
StepHypRef Expression
1 ax-5 1768 . 2  |-  ( ph  ->  A. x ph )
2 bj-spimevw.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spimeh 1851 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1673
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815
This theorem depends on definitions:  df-bi 190  df-ex 1674
This theorem is referenced by: (None)
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