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Theorem nfcjust 2559
Description: Justification theorem for df-nfc 2560. (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 1629 . . 3  |-  F/ x  y  =  z
2 eleq1 2495 . . 3  |-  ( y  =  z  ->  (
y  e.  A  <->  z  e.  A ) )
31, 2nfbidf 1790 . 2  |-  ( y  =  z  ->  ( F/ x  y  e.  A 
<->  F/ x  z  e.  A ) )
43cbvalv 1984 1  |-  ( A. y F/ x  y  e.  A  <->  A. z F/ x  z  e.  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   A.wal 1549   F/wnf 1553    e. wcel 1725
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-cleq 2428  df-clel 2431
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