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Theorem a16nfwAUX7 29622
Description: Weak version of a16nf 2054 not requiring ax-7 1750. (Contributed by NM, 10-Oct-2017.)
Assertion
Ref Expression
a16nfwAUX7  |-  ( A. x  x  =  y  ->  F/ z ph )
Distinct variable groups:    x, y    x, z
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem a16nfwAUX7
StepHypRef Expression
1 nfaewAUX7 29554 . 2  |-  F/ z A. x  x  =  y
2 a16gNEW7 29620 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
31, 2nfd 1783 1  |-  ( A. x  x  =  y  ->  F/ z ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550   F/wnf 1554
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762  ax-12 1951  ax-7v 29516
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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