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Theorem bj-axc16b 31459
Description: Remove dependency on ax-13 2102 from axc16b 4612. (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-axc16b  |-  ( A. x  x  =  y  ->  ( ph  ->  A. x ph ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem bj-axc16b
StepHypRef Expression
1 bj-dtru 31458 . 2  |-  -.  A. x  x  =  y
21pm2.21i 136 1  |-  ( A. x  x  =  y  ->  ( ph  ->  A. x ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-8 1900  ax-9 1907  ax-10 1926  ax-11 1931  ax-12 1944  ax-nul 4550  ax-pow 4598
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1458  df-ex 1675  df-nf 1679
This theorem is referenced by: (None)
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