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Theorem nfcjust 2270
Description: Justification theorem for df-nfc 2271. (Contributed by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
nfcjust  |-  ( A. y F/ x  y  e.  A  <->  A. z F/ x  z  e.  A )
Distinct variable groups:    x, y, z   
y, A, z
Allowed substitution hint:    A( x)

Proof of Theorem nfcjust
StepHypRef Expression
1 nfv 1509 . . 3  |-  F/ x  y  =  z
2 eleq1 2203 . . 3  |-  ( y  =  z  ->  (
y  e.  A  <->  z  e.  A ) )
31, 2nfbidf 1520 . 2  |-  ( y  =  z  ->  ( F/ x  y  e.  A 
<->  F/ x  z  e.  A ) )
43cbvalv 1890 1  |-  ( A. y F/ x  y  e.  A  <->  A. z F/ x  z  e.  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   A.wal 1330   F/wnf 1437    e. wcel 1481
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-cleq 2133  df-clel 2136
This theorem is referenced by: (None)
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