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Theorem nfnfc 2313
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 2295 . 2  |-  ( F/_ y A  <->  A. z F/ y  z  e.  A )
2 nfnfc.1 . . . . 5  |-  F/_ x A
32nfcri 2300 . . . 4  |-  F/ x  z  e.  A
43nfnf 1564 . . 3  |-  F/ x F/ y  z  e.  A
54nfal 1563 . 2  |-  F/ x A. z F/ y  z  e.  A
61, 5nfxfr 1461 1  |-  F/ x F/_ y A
Colors of variables: wff set class
Syntax hints:   A.wal 1340   F/wnf 1447    e. wcel 2135   F/_wnfc 2293
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-cleq 2157  df-clel 2160  df-nfc 2295
This theorem is referenced by: (None)
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