Theorem anim12i

Description: Conjoin antecedents and consequents of two premises. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 14-Dec-2013)

	Ref	Expression
Hypotheses	anim12i.1	|- ( ph -> ps )
	anim12i.2	|- ( ch -> th )
Assertion	anim12i	|- ( ( ph /\ ch ) -> ( ps /\ th ) )

Proof

Step	Hyp	Ref	Expression
1		anim12i.1	|- ( ph -> ps )
2		anim12i.2	|- ( ch -> th )
3		id	|- ( ( ps /\ th ) -> ( ps /\ th ) )
4	1 2 3	syl2an	|- ( ( ph /\ ch ) -> ( ps /\ th ) )