Theorem anim12

Description: Conjoin antecedents and consequents of two premises. This is the closed theorem form of anim12d . Theorem *3.47 of WhiteheadRussell p. 113. It was proved by Leibniz, and it evidently pleased him enough to call it praeclarum theorema (splendid theorem). (Contributed by NM, 12-Aug-1993) (Proof shortened by Wolf Lammen, 7-Apr-2013)

	Ref	Expression
Assertion	anim12	|- ( ( ( ph -> ps ) /\ ( ch -> th ) ) -> ( ( ph /\ ch ) -> ( ps /\ th ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ( ph -> ps ) -> ( ph -> ps ) )
2		id	|- ( ( ch -> th ) -> ( ch -> th ) )
3	1 2	im2anan9	|- ( ( ( ph -> ps ) /\ ( ch -> th ) ) -> ( ( ph /\ ch ) -> ( ps /\ th ) ) )