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Theorem nfnfc 2200
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 2183 . 2  |-  ( F/_ y A  <->  A. z F/ y  z  e.  A )
2 nfnfc.1 . . . . 5  |-  F/_ x A
32nfcri 2188 . . . 4  |-  F/ x  z  e.  A
43nfnf 1485 . . 3  |-  F/ x F/ y  z  e.  A
54nfal 1484 . 2  |-  F/ x A. z F/ y  z  e.  A
61, 5nfxfr 1379 1  |-  F/ x F/_ y A
Colors of variables: wff set class
Syntax hints:   A.wal 1257   F/wnf 1365    e. wcel 1409   F/_wnfc 2181
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-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-cleq 2049  df-clel 2052  df-nfc 2183
This theorem is referenced by: (None)
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