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Theorem axc16 2034
Description: Proof of older axiom ax-c16 32508. (Contributed by NM, 8-Nov-2006.) (Revised by NM, 22-Sep-2017.)
Assertion
Ref Expression
axc16  |-  ( A. x  x  =  y  ->  ( ph  ->  A. x ph ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem axc16
StepHypRef Expression
1 axc16g 2033 1  |-  ( A. x  x  =  y  ->  ( ph  ->  A. x ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674
This theorem is referenced by:  axc16nf  2037  ax12vALT  2267  hbs1  2275  exists2  2401  bj-ax6elem1  31308
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