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Theorem ax12dgen1 1740
Description: Degenerate instance of ax-12 1950 where bundled variables  x and  y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax12dgen1  |-  ( -.  x  =  x  -> 
( x  =  z  ->  A. x  x  =  z ) )

Proof of Theorem ax12dgen1
StepHypRef Expression
1 equid 1688 . 2  |-  x  =  x
21pm2.24i 138 1  |-  ( -.  x  =  x  -> 
( x  =  z  ->  A. x  x  =  z ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549
This theorem is referenced by:  ax12dgen4  1743
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
This theorem depends on definitions:  df-bi 178  df-ex 1551
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