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Theorem elequ1 1597
 Description: An identity law for the non-logical predicate. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elequ1 (x = y → (x zy z))

Proof of Theorem elequ1
StepHypRef Expression
1 ax-13 1401 . 2 (x = y → (x zy z))
2 ax-13 1401 . . 3 (y = x → (y zx z))
32equcoms 1591 . 2 (x = y → (y zx z))
41, 3impbid 120 1 (x = y → (x zy z))
 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-13 1401  ax-17 1416  ax-i9 1420 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  cleljust  1810  elsb3  1849  dveel1  1893  nalset  3878  zfpow  3919  mss  3953  zfun  4137  bj-nalset  9326  bj-nnelirr  9387
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