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Theorem bj-sbime 11320
Description: A strengthening of sbie 1721 (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 1457 . 2  |-  ( ps 
->  A. x ps )
3 bj-sbime.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
42, 3bj-sbimeh 11319 1  |-  ( [ y  /  x ] ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1394   [wsb 1692
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693
This theorem is referenced by:  setindis  11508  bdsetindis  11510
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