Theorem ad5ant2345

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017)

	Ref	Expression
Hypothesis	ad5ant2345.1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
Assertion	ad5ant2345	|- ( ( ( ( ( et /\ ph ) /\ ps ) /\ ch ) /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		ad5ant2345.1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
2	1	exp41	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
3	2	adantl	|- ( ( et /\ ph ) -> ( ps -> ( ch -> ( th -> ta ) ) ) )
4	3	imp41	|- ( ( ( ( ( et /\ ph ) /\ ps ) /\ ch ) /\ th ) -> ta )