Metamath Proof Explorer


Theorem ad5ant14

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 14-Apr-2022)

Ref Expression
Hypothesis ad5ant2.1
|- ( ( ph /\ ps ) -> ch )
Assertion ad5ant14
|- ( ( ( ( ( ph /\ th ) /\ ta ) /\ ps ) /\ et ) -> ch )

Proof

Step Hyp Ref Expression
1 ad5ant2.1
 |-  ( ( ph /\ ps ) -> ch )
2 1 adantlr
 |-  ( ( ( ph /\ th ) /\ ps ) -> ch )
3 2 ad4ant13
 |-  ( ( ( ( ( ph /\ th ) /\ ta ) /\ ps ) /\ et ) -> ch )