Theorem nfnfc1 2222

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 2208	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1476	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1508	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1403	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1282   F/wnf 1389   e. wcel 1433   F/_wnfc 2206

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-4 1440  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-nfc 2208

This theorem is referenced by:  vtoclgft  2649  sbcralt  2890  sbcrext  2891  csbiebt  2942  nfopd  3587  nfimad  4697  nffvd  5207