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Theorem bj-spimvv 31388
Description: Version of spimv 2114 and spimv1 2077 with a dv condition, which does not require ax-13 2104. UPDATE: this is spimvw 1851. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-spimvv.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-spimvv  |-  ( A. x ph  ->  ps )
Distinct variable groups:    x, y    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem bj-spimvv
StepHypRef Expression
1 ax6ev 1815 . . 3  |-  E. x  x  =  y
2 bj-spimvv.1 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2eximii 1717 . 2  |-  E. x
( ph  ->  ps )
4319.36iv 1829 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813
This theorem depends on definitions:  df-bi 190  df-ex 1672
This theorem is referenced by:  bj-spvv  31390  bj-aev  31420  bj-el  31477
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