Theorem 3adantl2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Hypothesis	3adantl.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion	3adantl2	|- ( ( ( ph /\ ta /\ ps ) /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		3adantl.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
2		3simpb	|- ( ( ph /\ ta /\ ps ) -> ( ph /\ ps ) )
3	2 1	sylan	|- ( ( ( ph /\ ta /\ ps ) /\ ch ) -> th )