Theorem nfnfc1 2258

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 2244	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1506	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1538	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1433	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1312   F/wnf 1419   e. wcel 1463   F/_wnfc 2242

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 1406  ax-7 1407  ax-gen 1408  ax-4 1470  ax-ial 1497

This theorem depends on definitions:  df-bi 116  df-nf 1420  df-nfc 2244

This theorem is referenced by:  vtoclgft  2707  sbcralt  2953  sbcrext  2954  csbiebt  3005  nfopd  3688  nfimad  4848  nffvd  5387