Metamath Proof Explorer

Theorem 3ad2ant2

Description: Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005)

Ref Expression
Hypothesis 3ad2ant.1 
|- ( ph -> ch )
Assertion 3ad2ant2 
|- ( ( ps /\ ph /\ th ) -> ch )

Proof

Step Hyp Ref Expression
1 3ad2ant.1 
 |-  ( ph -> ch )
2 1 adantr 
 |-  ( ( ph /\ th ) -> ch )
3 2 3adant1 
 |-  ( ( ps /\ ph /\ th ) -> ch )