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Theorem nd5 1677
 Description: A lemma for proving conditionless ZFC axioms. (Contributed by NM, 8-Jan-2002.)
Assertion
Ref Expression
nd5 y y = x → (z = yx z = y))
Distinct variable group:   x,z

Proof of Theorem nd5
StepHypRef Expression
1 dveeq2 1674 . 2 x x = y → (z = yx z = y))
21nalequcoms 1387 1 y y = x → (z = yx z = y))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1224   = wceq 1226 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-nf 1326  df-sb 1624 This theorem is referenced by: (None)
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