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Theorem ax9from9o 2148
Description: Rederivation of axiom ax-9 1654 from ax-9o 2138 and other older axioms. See ax9o 1950 for the derivation of ax-9o 2138 from ax-9 1654. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax9from9o ¬ x ¬ x = y

Proof of Theorem ax9from9o
StepHypRef Expression
1 ax-9o 2138 . 2 (x(x = yx ¬ x ¬ x = y) → ¬ x ¬ x = y)
2 ax-6o 2137 . . 3 x ¬ x ¬ x = y → ¬ x = y)
32con4i 122 . 2 (x = yx ¬ x ¬ x = y)
41, 3mpg 1548 1 ¬ x ¬ x = y
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-6o 2137  ax-9o 2138
This theorem is referenced by:  equidqe  2173
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