Metamath Proof Explorer


Theorem 3adant2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995)

Ref Expression
Hypothesis 3adant.1
|- ( ( ph /\ ps ) -> ch )
Assertion 3adant2
|- ( ( ph /\ th /\ ps ) -> ch )

Proof

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