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Theorem bj-sbimeh 13148
Description: A strengthening of sbieh 1764 (same proof). (Contributed by BJ, 16-Dec-2019.)
Hypotheses
Ref Expression
bj-sbimeh.1  |-  ( ps 
->  A. x ps )
bj-sbimeh.2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-sbimeh  |-  ( [ y  /  x ] ph  ->  ps )

Proof of Theorem bj-sbimeh
StepHypRef Expression
1 tru 1336 . . . 4  |- T.
21hbth 1440 . . 3  |-  ( T. 
->  A. x T.  )
3 bj-sbimeh.1 . . . 4  |-  ( ps 
->  A. x ps )
43a1i 9 . . 3  |-  ( T. 
->  ( ps  ->  A. x ps ) )
5 bj-sbimeh.2 . . . 4  |-  ( x  =  y  ->  ( ph  ->  ps ) )
65a1i 9 . . 3  |-  ( T. 
->  ( x  =  y  ->  ( ph  ->  ps ) ) )
72, 4, 6bj-sbimedh 13147 . 2  |-  ( T. 
->  ( [ y  /  x ] ph  ->  ps ) )
87mptru 1341 1  |-  ( [ y  /  x ] ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1330   T. wtru 1333   [wsb 1736
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-ial 1515
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-sb 1737
This theorem is referenced by:  bj-sbime  13149
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