Theorem 3anassrs

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017)

	Ref	Expression
Hypothesis	3anassrs.1	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
Assertion	3anassrs	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		3anassrs.1	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
2	1	3exp2	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
3	2	imp41	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )