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Theorem a16gbNEW7 29474
Description: A generalization of axiom ax-16 2220. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
a16gbNEW7  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem a16gbNEW7
StepHypRef Expression
1 a16gNEW7 29473 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
2 sp 1763 . 2  |-  ( A. z ph  ->  ph )
31, 2impbid1 195 1  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549
This theorem is referenced by:  sbalNEW7  29543
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950  ax-7v 29369
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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