Theorem nfnfc1 2181

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 2167	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1436	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1468	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1363	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1241   F/wnf 1349   e. wcel 1393   F/_wnfc 2165

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-nfc 2167

This theorem is referenced by:  vtoclgft  2604  sbcralt  2834  sbcrext  2835  csbiebt  2886  nfopd  3566  nfimad  4677  nffvd  5187