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

Theorem equidqeOLD 1356
 Description: Obsolete proof of equidqe 1355 as of 27-Feb-2014. (Contributed by NM, 13-Jan-2011.)
Assertion
Ref Expression
equidqeOLD ¬ y ¬ x = x

Proof of Theorem equidqeOLD
StepHypRef Expression
1 ax-9 1354 . 2 ¬ y ¬ y = x
2 ax-8 1328 . . . . . 6 (y = x → (y = xx = x))
32pm2.43i 41 . . . . 5 (y = xx = x)
43con3i 542 . . . 4 x = x → ¬ y = x)
54ax-gen 1269 . . 3 yx = x → ¬ y = x)
6 ax-5 1267 . . 3 (yx = x → ¬ y = x) → (y ¬ x = xy ¬ y = x))
75, 6ax-mp 7 . 2 (y ¬ x = xy ¬ y = x)
81, 7mto 566 1 ¬ y ¬ x = x
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1266 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
 Copyright terms: Public domain W3C validator