Theorem nfnfc1 2315

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 2301	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 1537	. . 3 |- F/ x F/ x y e. A
3	2	nfal 1569	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1467	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1346   F/wnf 1453   e. wcel 2141   F/_wnfc 2299

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-nfc 2301

This theorem is referenced by:  vtoclgft  2780  sbcralt  3031  sbcrext  3032  csbiebt  3088  nfopd  3782  nfimad  4962  nffvd  5508