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Theorem nfnfc 2585
Description: Hypothesis builder for  F/_ y A. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfnfc.1  |-  F/_ x A
Assertion
Ref Expression
nfnfc  |-  F/ x F/_ y A

Proof of Theorem nfnfc
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2568 . 2  |-  ( F/_ y A  <->  A. z F/ y  z  e.  A )
2 nfnfc.1 . . . . 5  |-  F/_ x A
32nfcri 2573 . . . 4  |-  F/ x  z  e.  A
43nfnf 1875 . . 3  |-  F/ x F/ y  z  e.  A
54nfal 1873 . 2  |-  F/ x A. z F/ y  z  e.  A
61, 5nfxfr 1615 1  |-  F/ x F/_ y A
Colors of variables: wff setvar class
Syntax hints:   A.wal 1367   F/wnf 1589    e. wcel 1756   F/_wnfc 2566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1587  df-nf 1590  df-sb 1701  df-cleq 2436  df-clel 2439  df-nfc 2568
This theorem is referenced by: (None)
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