Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbequ6 Structured version   GIF version

Theorem sbequ6 1644
 Description: Substitution does not change a distinctor. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 14-May-2005.)
Assertion
Ref Expression
sbequ6 ([w / z] ¬ x x = y ↔ ¬ x x = y)

Proof of Theorem sbequ6
StepHypRef Expression
1 nfnae 1588 . 2 z ¬ x x = y
21sbf 1638 1 ([w / z] ¬ x x = y ↔ ¬ x x = y)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ↔ wb 98  ∀wal 1224  [wsb 1623 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 532  ax-in2 533  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405 This theorem depends on definitions:  df-bi 110  df-tru 1229  df-fal 1232  df-nf 1326  df-sb 1624 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator