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Theorem ax12dgen2 1742
Description: Degenerate instance of ax-12 1951 where bundled variables  x and  z have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax12dgen2  |-  ( -.  x  =  y  -> 
( y  =  x  ->  A. x  y  =  x ) )

Proof of Theorem ax12dgen2
StepHypRef Expression
1 equcomi 1692 . 2  |-  ( y  =  x  ->  x  =  y )
2 pm2.21 103 . 2  |-  ( -.  x  =  y  -> 
( x  =  y  ->  A. x  y  =  x ) )
31, 2syl5 31 1  |-  ( -.  x  =  y  -> 
( y  =  x  ->  A. x  y  =  x ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688
This theorem depends on definitions:  df-bi 179  df-ex 1552
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