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Theorem nfnfc 2425
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 2408 . 2  |-  ( F/_ y A  <->  A. z F/ y  z  e.  A )
2 nfnfc.1 . . . . 5  |-  F/_ x A
32nfcri 2413 . . . 4  |-  F/ x  z  e.  A
43nfnf 1768 . . 3  |-  F/ x F/ y  z  e.  A
54nfal 1766 . 2  |-  F/ x A. z F/ y  z  e.  A
61, 5nfxfr 1557 1  |-  F/ x F/_ y A
Colors of variables: wff set class
Syntax hints:   A.wal 1527   F/wnf 1531    e. wcel 1684   F/_wnfc 2406
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-cleq 2276  df-clel 2279  df-nfc 2408
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