Theorem syldan

Description: A syllogism deduction with conjoined antecedents. (Contributed by NM, 24-Feb-2005) (Proof shortened by Wolf Lammen, 6-Apr-2013)

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

Proof

Step	Hyp	Ref	Expression
1		syldan.1	|- ( ( ph /\ ps ) -> ch )
2		syldan.2	|- ( ( ph /\ ch ) -> th )
3		simpl	|- ( ( ph /\ ps ) -> ph )
4	3 1 2	syl2anc	|- ( ( ph /\ ps ) -> th )