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Theorem equid1ALT 2176
 Description: Identity law for equality (reflexivity). Lemma 6 of [Tarski] p. 68. Alternate proof of equid1 2158 from older axioms ax-6o 2137 and ax-9o 2138. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equid1ALT x = x

Proof of Theorem equid1ALT
StepHypRef Expression
1 ax-12o 2142 . . . . 5 x x = x → (¬ x x = x → (x = xx x = x)))
21pm2.43i 43 . . . 4 x x = x → (x = xx x = x))
32alimi 1559 . . 3 (x ¬ x x = xx(x = xx x = x))
4 ax-9o 2138 . . 3 (x(x = xx x = x) → x = x)
53, 4syl 15 . 2 (x ¬ x x = xx = x)
6 ax-6o 2137 . 2 x ¬ x x = xx = x)
75, 6pm2.61i 156 1 x = 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-6o 2137  ax-9o 2138  ax-12o 2142 This theorem is referenced by: (None)
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