Theorem nfci 2480

Description: Deduce that a class A does not have x free in it. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfci.1	|- F/x y e. A

Assertion

Ref	Expression
nfci	|- F/_xA

Distinct variable groups:   x,y   y,A

Allowed substitution hint:   A(x)

Proof of Theorem nfci

Step	Hyp	Ref	Expression
1		df-nfc 2479	. 2 |- ( F/_xA <-> A.y F/x y e. A)
2		nfci.1	. 2 |- F/x y e. A
3	1, 2	mpgbir 1550	1 |- F/_xA

Syntax hints:   F/wnf 1544   e. wcel 1710   F/_wnfc 2477

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546

This theorem depends on definitions:  df-bi 177  df-nfc 2479

This theorem is referenced by:  nfcii  2481  nfcv  2490  nfab1  2492  nfab  2494