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Theorem nd5 1699
Description: A lemma for proving conditionless ZFC axioms. (Contributed by NM, 8-Jan-2002.)
Assertion
Ref Expression
nd5  |-  ( -. 
A. y  y  =  x  ->  ( z  =  y  ->  A. x  z  =  y )
)
Distinct variable group:    x, z

Proof of Theorem nd5
StepHypRef Expression
1 dveeq2 1696 . 2  |-  ( -. 
A. x  x  =  y  ->  ( z  =  y  ->  A. x  z  =  y )
)
21nalequcoms 1410 1  |-  ( -. 
A. y  y  =  x  ->  ( z  =  y  ->  A. x  z  =  y )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1241    = wceq 1243
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 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646
This theorem is referenced by: (None)
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