Metamath Proof Explorer


Theorem ad5antlr

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

Ref Expression
Hypothesis ad2ant.1
|- ( ph -> ps )
Assertion ad5antlr
|- ( ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )

Proof

Step Hyp Ref Expression
1 ad2ant.1
 |-  ( ph -> ps )
2 1 adantl
 |-  ( ( ch /\ ph ) -> ps )
3 2 ad4antr
 |-  ( ( ( ( ( ( ch /\ ph ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )