Theorem ad5ant125

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 23-Jun-2022)

	Ref	Expression
Hypothesis	ad5ant.1	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	ad5ant125	|- ( ( ( ( ( ph /\ ps ) /\ ta ) /\ et ) /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		ad5ant.1	|- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expia	|- ( ( ph /\ ps ) -> ( ch -> th ) )
3	2	2a1d	|- ( ( ph /\ ps ) -> ( ta -> ( et -> ( ch -> th ) ) ) )
4	3	imp41	|- ( ( ( ( ( ph /\ ps ) /\ ta ) /\ et ) /\ ch ) -> th )