Metamath Proof Explorer

Theorem ad4antr

Description: Deduction adding 4 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)

Ref Expression
Hypothesis ad2ant.1 
|- ( ph -> ps )
Assertion ad4antr 
|- ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )

Proof

Step Hyp Ref Expression
1 ad2ant.1 
 |-  ( ph -> ps )
2 1 adantr 
 |-  ( ( ph /\ ch ) -> ps )
3 2 ad3antrrr 
 |-  ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )