Theorem nfcd

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

	Ref	Expression
Hypotheses	nfcd.1	|- F/ y ph
	nfcd.2	|- ( ph -> F/ x y e. A )
Assertion	nfcd	|- ( ph -> F/_ x A )

Proof

Step	Hyp	Ref	Expression
1		nfcd.1	|- F/ y ph
2		nfcd.2	|- ( ph -> F/ x y e. A )
3	1 2	alrimi	|- ( ph -> A. y F/ x y e. A )
4		df-nfc	|- ( F/_ x A <-> A. y F/ x y e. A )
5	3 4	sylibr	|- ( ph -> F/_ x A )