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Theorem ax-12 1340
Description: Rederive the original version of the axiom from ax-i12 1336. (Contributed by Mario Carneiro, 3-Feb-2015.)
Assertion
Ref Expression
ax-12 z z = x → (¬ z z = y → (x = yz x = y)))

Proof of Theorem ax-12
StepHypRef Expression
1 ax-i12 1336 . . . 4 (z z = x (z z = y z(x = yz x = y)))
21ori 621 . . 3 z z = x → (z z = y z(x = yz x = y)))
32ord 622 . 2 z z = x → (¬ z z = yz(x = yz x = y)))
4 ax-4 1338 . 2 (z(x = yz x = y) → (x = yz x = y))
53, 4syl6 27 1 z z = x → (¬ z z = y → (x = yz x = y)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 609  wal 1271   = wceq 1329
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-in2 528  ax-io 610  ax-i12 1336  ax-4 1338
This theorem depends on definitions:  df-bi 108
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