Metamath Proof Explorer

Theorem ad2antlr

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999) (Proof shortened by Wolf Lammen, 20-Nov-2012)

Ref Expression
Hypothesis ad2ant.1 
|- ( ph -> ps )
Assertion ad2antlr 
|- ( ( ( ch /\ ph ) /\ th ) -> ps )

Proof

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