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Theorem nd4 8212
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 8211 . 2  |-  ( A. y  y  =  x  ->  -.  A. z  y  e.  x )
21aecoms 1887 1  |-  ( A. x  x  =  y  ->  -.  A. z  y  e.  x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527    e. wcel 1684
This theorem is referenced by:  axrepnd  8216
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-reg 7306
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-v 2790  df-dif 3155  df-un 3157  df-nul 3456  df-sn 3646  df-pr 3647
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