Theorem nfnfc1 2351

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 2337	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1567	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1599	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1497	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1371   F/wnf 1483   e. wcel 2176   F/_wnfc 2335

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 1470  ax-7 1471  ax-gen 1472  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-nfc 2337

This theorem is referenced by:  vtoclgft  2823  sbcralt  3075  sbcrext  3076  csbiebt  3133  nfopd  3836  nfimad  5031  nffvd  5588