Metamath Proof Explorer

Theorem ad2ant2r

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 8-Jan-2006)

Ref Expression
Hypothesis ad2ant2.1 
|- ( ( ph /\ ps ) -> ch )
Assertion ad2ant2r 
|- ( ( ( ph /\ th ) /\ ( ps /\ ta ) ) -> ch )

Proof

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