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Theorem nfnfc 2578
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 2561 . 2  |-  ( F/_ y A  <->  A. z F/ y  z  e.  A )
2 nfnfc.1 . . . . 5  |-  F/_ x A
32nfcri 2566 . . . 4  |-  F/ x  z  e.  A
43nfnf 1867 . . 3  |-  F/ x F/ y  z  e.  A
54nfal 1864 . 2  |-  F/ x A. z F/ y  z  e.  A
61, 5nfxfr 1579 1  |-  F/ x F/_ y A
Colors of variables: wff set class
Syntax hints:   A.wal 1549   F/wnf 1553    e. wcel 1725   F/_wnfc 2559
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 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2429  df-clel 2432  df-nfc 2561
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