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Theorem nfcjust 2216
Description: Justification theorem for df-nfc 2217. (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 1466 . . 3  |-  F/ x  y  =  z
2 eleq1 2150 . . 3  |-  ( y  =  z  ->  (
y  e.  A  <->  z  e.  A ) )
31, 2nfbidf 1477 . 2  |-  ( y  =  z  ->  ( F/ x  y  e.  A 
<->  F/ x  z  e.  A ) )
43cbvalv 1842 1  |-  ( A. y F/ x  y  e.  A  <->  A. z F/ x  z  e.  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   A.wal 1287   F/wnf 1394    e. wcel 1438
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-cleq 2081  df-clel 2084
This theorem is referenced by: (None)
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