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Theorem nfnfc 2181
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 2164 . 2 (yAzy z A)
2 nfnfc.1 . . . . 5 xA
32nfcri 2169 . . . 4 x z A
43nfnf 1466 . . 3 xy z A
54nfal 1465 . 2 xzy z A
61, 5nfxfr 1360 1 xyA
Colors of variables: wff set class
Syntax hints:  wal 1240  wnf 1346   wcel 1390  wnfc 2162
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164
This theorem is referenced by: (None)
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