Theorem nfnfc1 2353

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 2339	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1568	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1600	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1498	1 |- F/ x F/_ x 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-5 1471  ax-7 1472  ax-gen 1473  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-nfc 2339

This theorem is referenced by:  vtoclgft  2828  sbcralt  3082  sbcrext  3083  csbiebt  3141  nfopd  3850  nfimad  5050  nffvd  5611