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Theorem nfcjust 2182
Description: Justification theorem for df-nfc 2183. (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 1437 . . 3  |-  F/ x  y  =  z
2 eleq1 2116 . . 3  |-  ( y  =  z  ->  (
y  e.  A  <->  z  e.  A ) )
31, 2nfbidf 1448 . 2  |-  ( y  =  z  ->  ( F/ x  y  e.  A 
<->  F/ x  z  e.  A ) )
43cbvalv 1810 1  |-  ( A. y F/ x  y  e.  A  <->  A. z F/ x  z  e.  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 102   A.wal 1257   F/wnf 1365    e. wcel 1409
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-cleq 2049  df-clel 2052
This theorem is referenced by: (None)
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