Theorem im2anan9

Description: Deduction joining nested implications to form implication of conjunctions. (Contributed by NM, 29-Feb-1996)

	Ref	Expression
Hypotheses	im2an9.1	|- ( ph -> ( ps -> ch ) )
	im2an9.2	|- ( th -> ( ta -> et ) )
Assertion	im2anan9	|- ( ( ph /\ th ) -> ( ( ps /\ ta ) -> ( ch /\ et ) ) )

Proof

Step	Hyp	Ref	Expression
1		im2an9.1	|- ( ph -> ( ps -> ch ) )
2		im2an9.2	|- ( th -> ( ta -> et ) )
3	1	adantrd	|- ( ph -> ( ( ps /\ ta ) -> ch ) )
4	2	adantld	|- ( th -> ( ( ps /\ ta ) -> et ) )
5	3 4	anim12ii	|- ( ( ph /\ th ) -> ( ( ps /\ ta ) -> ( ch /\ et ) ) )