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Theorem nd4 8465
Description: A lemma for proving conditionless ZFC axioms. (Contributed by NM, 2-Jan-2002.)
Assertion
Ref Expression
nd4  |-  ( A. x  x  =  y  ->  -.  A. z  y  e.  x )

Proof of Theorem nd4
StepHypRef Expression
1 nd3 8464 . 2  |-  ( A. y  y  =  x  ->  -.  A. z  y  e.  x )
21aecoms 2036 1  |-  ( A. x  x  =  y  ->  -.  A. z  y  e.  x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549
This theorem is referenced by:  axrepnd  8469
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403  ax-reg 7560
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-v 2958  df-dif 3323  df-un 3325  df-nul 3629  df-sn 3820  df-pr 3821
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