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Theorem nd4 8228
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 8227 . 2  |-  ( A. y  y  =  x  ->  -.  A. z  y  e.  x )
21aecoms 1900 1  |-  ( A. x  x  =  y  ->  -.  A. z  y  e.  x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530    e. wcel 1696
This theorem is referenced by:  axrepnd  8232
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230  ax-reg 7322
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-v 2803  df-dif 3168  df-un 3170  df-nul 3469  df-sn 3659  df-pr 3660
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