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Theorem bj-sbime 14713
Description: A strengthening of sbie 1791 (same proof). (Contributed by BJ, 16-Dec-2019.)
Hypotheses
Ref Expression
bj-sbime.nf  |-  F/ x ps
bj-sbime.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-sbime  |-  ( [ y  /  x ] ph  ->  ps )

Proof of Theorem bj-sbime
StepHypRef Expression
1 bj-sbime.nf . . 3  |-  F/ x ps
21nfri 1519 . 2  |-  ( ps 
->  A. x ps )
3 bj-sbime.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
42, 3bj-sbimeh 14712 1  |-  ( [ y  /  x ] ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1460   [wsb 1762
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763
This theorem is referenced by:  setindis  14907  bdsetindis  14909
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