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Theorem ax12v 1951
Description: A weaker version of ax-12 1950 with distinct variable restrictions on pairs  x ,  z and  y ,  z. In order to show that this weakening is adequate, this should be the only theorem referencing ax-12 1950 directly. (Contributed by NM, 30-Jun-2016.)
Assertion
Ref Expression
ax12v  |-  ( -.  x  =  y  -> 
( y  =  z  ->  A. x  y  =  z ) )
Distinct variable groups:    x, z    y, z

Proof of Theorem ax12v
StepHypRef Expression
1 ax-12 1950 1  |-  ( -.  x  =  y  -> 
( y  =  z  ->  A. x  y  =  z ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549
This theorem is referenced by:  a9e  1952  ax12olem2  2006  nfeqf  2009  ax12oOLD  2018  ax12oNEW7  29461
This theorem was proved from axioms:  ax-12 1950
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