Theorem nfan

Description: If x is not free in ph and ps , then it is not free in ( ph /\ ps ) . (Contributed by Mario Carneiro, 11-Aug-2016) (Proof shortened by Wolf Lammen, 13-Jan-2018) (Proof shortened by Wolf Lammen, 9-Oct-2021)

	Ref	Expression
Hypotheses	nfan.1	|- F/ x ph
	nfan.2	|- F/ x ps
Assertion	nfan	|- F/ x ( ph /\ ps )

Proof

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