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Theorem ax12dgen2 1726
Description: Degenerate instance of ax-12 1925 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 = xx y = x))

Proof of Theorem ax12dgen2
StepHypRef Expression
1 equcomi 1679 . 2 (y = xx = y)
2 pm2.21 100 . 2 x = y → (x = yx y = x))
31, 2syl5 28 1 x = y → (y = xx y = x))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by: (None)
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