Theorem nfnfc1 2238

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 2224	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1488	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1520	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1415	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1294   F/wnf 1401   e. wcel 1445   F/_wnfc 2222

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-7 1389  ax-gen 1390  ax-4 1452  ax-ial 1479

This theorem depends on definitions:  df-bi 116  df-nf 1402  df-nfc 2224

This theorem is referenced by:  vtoclgft  2683  sbcralt  2929  sbcrext  2930  csbiebt  2981  nfopd  3661  nfimad  4816  nffvd  5352