Theorem nfnfc 2357

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 2339	. 2 |- ( F/_ y A <-> A. z F/ y z e. A )
2		nfnfc.1	. . . . 5 |- F/_ x A
3	2	nfcri 2344	. . . 4 |- F/ x z e. A
4	3	nfnf 1601	. . 3 |- F/ x F/ y z e. A
5	4	nfal 1600	. 2 |- F/ x A. z F/ y z e. A
6	1, 5	nfxfr 1498	1 |- F/ x F/_ y A

Syntax hints:   A.wal 1371   F/wnf 1484   e. wcel 2178   F/_wnfc 2337

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-cleq 2200  df-clel 2203  df-nfc 2339

This theorem is referenced by: (None)