 Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  equidqe Structured version   GIF version

Theorem equidqe 1422
 Description: equid 1586 with some quantification and negation without using ax-4 1397 or ax-17 1416. (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 1421 . 2 ¬ y ¬ y = x
2 ax-8 1392 . . . . 5 (y = x → (y = xx = x))
32pm2.43i 43 . . . 4 (y = xx = x)
43con3i 561 . . 3 x = x → ¬ y = x)
54alimi 1341 . 2 (y ¬ x = xy ¬ y = x)
61, 5mto 587 1 ¬ y ¬ x = x
 Colors of variables: wff set class Syntax hints:  ¬ wn 3  ∀wal 1240 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-8 1392  ax-i9 1420 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248 This theorem is referenced by:  ax4sp1  1423
 Copyright terms: Public domain W3C validator