Metamath Proof Explorer

Theorem ad2antll

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 19-Oct-1999)

Ref Expression
Hypothesis ad2ant.1 
|- ( ph -> ps )
Assertion ad2antll 
|- ( ( ch /\ ( th /\ ph ) ) -> ps )

Proof

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