Theorem nfbi

Description: If x is not free in ph and ps , then it is not free in ( ph <-> ps ) . (Contributed by NM, 26-May-1993) (Revised by Mario Carneiro, 11-Aug-2016) (Proof shortened by Wolf Lammen, 2-Jan-2018)

	Ref	Expression
Hypotheses	nf.1	|- F/ x ph
	nf.2	|- F/ x ps
Assertion	nfbi	|- F/ x ( ph <-> ps )

Proof

Step	Hyp	Ref	Expression
1		nf.1	|- F/ x ph
2		nf.2	|- F/ x ps
3	1	a1i	|- ( T. -> F/ x ph )
4	2	a1i	|- ( T. -> F/ x ps )
5	3 4	nfbid	|- ( T. -> F/ x ( ph <-> ps ) )
6	5	mptru	|- F/ x ( ph <-> ps )