Theorem nfnfc 2236

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.

Step	Hyp	Ref	Expression
1		df-nfc 2218	. 2 |- ( F/_ y A <-> A. z F/ y z e. A )
2		nfnfc.1	. . . . 5 |- F/_ x A
3	2	nfcri 2223	. . . 4 |- F/ x z e. A
4	3	nfnf 1515	. . 3 |- F/ x F/ y z e. A
5	4	nfal 1514	. 2 |- F/ x A. z F/ y z e. A
6	1, 5	nfxfr 1409	1 |- F/ x F/_ y A

Syntax hints:   A.wal 1288   F/wnf 1395   e. wcel 1439   F/_wnfc 2216

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-cleq 2082  df-clel 2085  df-nfc 2218

This theorem is referenced by: (None)