Metamath Proof Explorer


Theorem 3ad2antl3

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007)

Ref Expression
Hypothesis 3ad2antl.1
|- ( ( ph /\ ch ) -> th )
Assertion 3ad2antl3
|- ( ( ( ps /\ ta /\ ph ) /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 3ad2antl.1
 |-  ( ( ph /\ ch ) -> th )
2 1 adantll
 |-  ( ( ( ta /\ ph ) /\ ch ) -> th )
3 2 3adantl1
 |-  ( ( ( ps /\ ta /\ ph ) /\ ch ) -> th )