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Theorem nfnfc 2166
Description: Hypothesis builder for yA. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfnfc.1 xA
Assertion
Ref Expression
nfnfc xyA

Proof of Theorem nfnfc
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2149 . 2 (yAzy z A)
2 nfnfc.1 . . . . 5 xA
32nfcri 2154 . . . 4 x z A
43nfnf 1451 . . 3 xy z A
54nfal 1450 . 2 xzy z A
61, 5nfxfr 1343 1 xyA
Colors of variables: wff set class
Syntax hints:  wal 1226  wnf 1329   wcel 1374  wnfc 2147
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-cleq 2015  df-clel 2018  df-nfc 2149
This theorem is referenced by: (None)
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