Theorem nfcii 2169

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

Hypothesis

Ref	Expression
nfcii.1	|- ( y e. A -> A. x y e. A )

Assertion

Ref	Expression
nfcii	|- F/_ x A

Distinct variable groups:   x, y   y, A

Allowed substitution hint:   A( x)

Proof of Theorem nfcii

Step	Hyp	Ref	Expression
1		nfcii.1	. . 3 |- ( y e. A -> A. x y e. A )
2	1	nfi 1351	. 2 |- F/ x y e. A
3	2	nfci 2168	1 |- F/_ x A

Syntax hints:   -> wi 4   A.wal 1241   e. wcel 1393   F/_wnfc 2165

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-nfc 2167

This theorem is referenced by: (None)