Theorem nfnfc 2336

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 2318	. 2 |- ( F/_ y A <-> A. z F/ y z e. A )
2		nfnfc.1	. . . . 5 |- F/_ x A
3	2	nfcri 2323	. . . 4 |- F/ x z e. A
4	3	nfnf 1587	. . 3 |- F/ x F/ y z e. A
5	4	nfal 1586	. 2 |- F/ x A. z F/ y z e. A
6	1, 5	nfxfr 1484	1 |- F/ x F/_ y A

Syntax hints:   A.wal 1361   F/wnf 1470   e. wcel 2158   F/_wnfc 2316

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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773  df-cleq 2180  df-clel 2183  df-nfc 2318

This theorem is referenced by: (None)