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Theorem nfcjust 2581
Description: Justification theorem for df-nfc 2582. (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 1765 . . 3  |-  F/ x  y  =  z
2 eleq1 2518 . . 3  |-  ( y  =  z  ->  (
y  e.  A  <->  z  e.  A ) )
31, 2nfbidf 1970 . 2  |-  ( y  =  z  ->  ( F/ x  y  e.  A 
<->  F/ x  z  e.  A ) )
43cbvalv 2117 1  |-  ( A. y F/ x  y  e.  A  <->  A. z F/ x  z  e.  A )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189   A.wal 1446   F/wnf 1671    e. wcel 1891
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1673  ax-4 1686  ax-5 1762  ax-6 1809  ax-7 1855  ax-10 1919  ax-11 1924  ax-12 1937  ax-13 2092  ax-ext 2432
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1668  df-nf 1672  df-cleq 2445  df-clel 2448
This theorem is referenced by: (None)
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