Theorem nfnfc1 2377

Description: x is bound in F/_ x A. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfnfc1	|- F/ x F/_ x A

Proof of Theorem nfnfc1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-nfc 2363	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1592	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1624	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1522	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1395   F/wnf 1508   e. wcel 2202   F/_wnfc 2361

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-5 1495  ax-7 1496  ax-gen 1497  ax-ial 1582

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-nfc 2363

This theorem is referenced by:  vtoclgft  2854  sbcralt  3108  sbcrext  3109  csbiebt  3167  nfopd  3879  nfimad  5085  nffvd  5651