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Theorem bj-stdpc4v 34754
Description: Version of stdpc4 2096 with a dv condition, which does not require ax-13 2004. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-stdpc4v  |-  ( A. x ph  ->  [ y  /  x ] ph )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem bj-stdpc4v
StepHypRef Expression
1 ax-1 6 . . 3  |-  ( ph  ->  ( x  =  y  ->  ph ) )
21alimi 1638 . 2  |-  ( A. x ph  ->  A. x
( x  =  y  ->  ph ) )
3 bj-sb2v 34753 . 2  |-  ( A. x ( x  =  y  ->  ph )  ->  [ y  /  x ] ph )
42, 3syl 16 1  |-  ( A. x ph  ->  [ y  /  x ] ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1396   [wsb 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-sb 1745
This theorem is referenced by:  bj-2stdpc4v  34755  bj-sbftv  34765  bj-sbtv  34767  bj-vexwvt  34852  bj-abfal  34894
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