Metamath Proof Explorer

Theorem ad5ant12

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017)

Ref Expression
Hypothesis ad5ant2.1 
|- ( ( ph /\ ps ) -> ch )
Assertion ad5ant12 
|- ( ( ( ( ( ph /\ ps ) /\ th ) /\ ta ) /\ et ) -> ch )

Proof

Step Hyp Ref Expression
1 ad5ant2.1 
 |-  ( ( ph /\ ps ) -> ch )
2 1 ad3antrrr 
 |-  ( ( ( ( ( ph /\ ps ) /\ th ) /\ ta ) /\ et ) -> ch )