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Theorem equidOLD 1677
 Description: Obsolete proof of equid 1676 as of 9-Dec-2017. (Contributed by NM, 1-Apr-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equidOLD x = x

Proof of Theorem equidOLD
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 ax9v 1655 . . 3 ¬ y ¬ y = x
2 ax-8 1675 . . . . . 6 (y = x → (y = xx = x))
32pm2.43i 43 . . . . 5 (y = xx = x)
43con3i 127 . . . 4 x = x → ¬ y = x)
54alimi 1559 . . 3 (y ¬ x = xy ¬ y = x)
61, 5mto 167 . 2 ¬ y ¬ x = x
7 ax-17 1616 . 2 x = xy ¬ x = x)
86, 7mt3 171 1 x = x
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3  ∀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 is referenced by: (None)
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