Theorem ad5antr

Description: Deduction adding 5 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	ad5antr	|- ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )

Proof

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