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Theorem bj-sbimeh 10734
Description: A strengthening of sbieh 1714 (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 1289 . . . 4  |- T.
21hbth 1393 . . 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 10733 . 2  |-  ( T. 
->  ( [ y  /  x ] ph  ->  ps ) )
87trud 1294 1  |-  ( [ y  /  x ] ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   T. wtru 1286   [wsb 1686
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-sb 1687
This theorem is referenced by:  bj-sbime  10735
  Copyright terms: Public domain W3C validator