Metamath Proof Explorer


Theorem ad2ant2rl

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 24-Nov-2007)

Ref Expression
Hypothesis ad2ant2.1
|- ( ( ph /\ ps ) -> ch )
Assertion ad2ant2rl
|- ( ( ( ph /\ th ) /\ ( ta /\ ps ) ) -> ch )

Proof

Step Hyp Ref Expression
1 ad2ant2.1
 |-  ( ( ph /\ ps ) -> ch )
2 1 adantrl
 |-  ( ( ph /\ ( ta /\ ps ) ) -> ch )
3 2 adantlr
 |-  ( ( ( ph /\ th ) /\ ( ta /\ ps ) ) -> ch )