Metamath Proof Explorer


Theorem ad7antr

Description: Deduction adding 7 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 ad7antr
|- ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> ps )

Proof

Step Hyp Ref Expression
1 ad2ant.1
 |-  ( ph -> ps )
2 1 adantr
 |-  ( ( ph /\ ch ) -> ps )
3 2 ad6antr
 |-  ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> ps )