Theorem 3adantl1

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

	Ref	Expression
Hypothesis	3adantl.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion	3adantl1	|- ( ( ( ta /\ ph /\ ps ) /\ ch ) -> th )

Proof

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