Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  elequ2 Structured version   GIF version

Theorem elequ2 1598
 Description: An identity law for the non-logical predicate. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elequ2 (x = y → (z xz y))

Proof of Theorem elequ2
StepHypRef Expression
1 ax-14 1402 . 2 (x = y → (z xz y))
2 ax-14 1402 . . 3 (y = x → (z yz x))
32equcoms 1591 . 2 (x = y → (z yz x))
41, 3impbid 120 1 (x = y → (z xz y))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98 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-gen 1335  ax-ie2 1380  ax-8 1392  ax-14 1402  ax-17 1416  ax-i9 1420 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  elsb4  1850  dveel2  1894  axext3  2020  axext4  2021  bm1.1  2022  bm1.3ii  3869  nalset  3878  zfun  4137  fv3  5140  tfrlemisucaccv  5880  bdsepnft  9321  bdsepnfALT  9323  bdbm1.3ii  9325  bj-nalset  9326  bj-nnelirr  9387  strcollnft  9414  strcollnfALT  9416
 Copyright terms: Public domain W3C validator