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Theorem equidqe 1355
 Description: equid 1475 with some quantification and negation without using ax-4 1333 or ax-17 1349. (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 27-Feb-2014.)
Assertion
Ref Expression
equidqe ¬ y ¬ x = x

Proof of Theorem equidqe
StepHypRef Expression
1 ax-9 1354 . 2 ¬ y ¬ y = x
2 ax-8 1328 . . . . 5 (y = x → (y = xx = x))
32pm2.43i 41 . . . 4 (y = xx = x)
43con3i 542 . . 3 x = x → ¬ y = x)
54alimi 1275 . 2 (y ¬ x = xy ¬ y = x)
61, 5mto 566 1 ¬ y ¬ x = x
 Colors of variables: wff set class Syntax hints:  ¬ wn 3  ∀wal 1266 This theorem is referenced by:  ax4sp1  1357 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-in1 526  ax-in2 527  ax-5 1267  ax-gen 1269  ax-ie2 1315  ax-8 1328  ax-i9 1353 This theorem depends on definitions:  df-bi 108  df-tru 1201  df-fal 1202
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