Theorem anim12ii

Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007) (Proof shortened by Wolf Lammen, 19-Jul-2013)

	Ref	Expression
Hypotheses	anim12ii.1	|- ( ph -> ( ps -> ch ) )
	anim12ii.2	|- ( th -> ( ps -> ta ) )
Assertion	anim12ii	|- ( ( ph /\ th ) -> ( ps -> ( ch /\ ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		anim12ii.1	|- ( ph -> ( ps -> ch ) )
2		anim12ii.2	|- ( th -> ( ps -> ta ) )
3		pm3.43	|- ( ( ( ps -> ch ) /\ ( ps -> ta ) ) -> ( ps -> ( ch /\ ta ) ) )
4	1 2 3	syl2an	|- ( ( ph /\ th ) -> ( ps -> ( ch /\ ta ) ) )