Metamath Proof Explorer


Theorem 3adant1r

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 23-Jun-2022)

Ref Expression
Hypothesis ad4ant3.1
|- ( ( ph /\ ps /\ ch ) -> th )
Assertion 3adant1r
|- ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 ad4ant3.1
 |-  ( ( ph /\ ps /\ ch ) -> th )
2 simpl
 |-  ( ( ph /\ ta ) -> ph )
3 2 1 syl3an1
 |-  ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )