Theorem 3anasss

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). Converse of 3anassrs . (Contributed by Thierry Arnoux, 5-Jul-2026)

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

Proof

Step	Hyp	Ref	Expression
1		3anasss.1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
2		13an22anass	|- ( ( ph /\ ( ps /\ ch /\ th ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )
3	1	anasss	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )
4	2 3	sylbi	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )