Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  a16nfwAUX7 Unicode version

Theorem a16nfwAUX7 29400
Description: Weak version of a16nf 2135 not requiring ax-7 1749. (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 29334 . 2  |-  F/ z A. x  x  =  y
2 a16gNEW7 29398 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
31, 2nfd 1782 1  |-  ( A. x  x  =  y  ->  F/ z ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   F/wnf 1553
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 29296
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
  Copyright terms: Public domain W3C validator