Metamath Proof Explorer

Theorem 3adant3r

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 25-Jun-2022)

Ref Expression
Hypothesis ad4ant3.1 
|- ( ( ph /\ ps /\ ch ) -> th )
Assertion 3adant3r 
|- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Proof

Step Hyp Ref Expression
1 ad4ant3.1 
 |-  ( ( ph /\ ps /\ ch ) -> th )
2 simpl 
 |-  ( ( ch /\ ta ) -> ch )
3 2 1 syl3an3 
 |-  ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )