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Theorem a16gb 1821
Description: A generalization of axiom ax-16 1770. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
a16gb  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem a16gb
StepHypRef Expression
1 a16g 1820 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
2 ax-4 1472 . 2  |-  ( A. z ph  ->  ph )
31, 2impbid1 141 1  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1314
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-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721
This theorem is referenced by: (None)
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