Theorem 3an4anass

Description: Associative law for four conjunctions with a triple conjunction. (Contributed by Alexander van der Vekens, 24-Jun-2018)

	Ref	Expression
Assertion	3an4anass	|- ( ( ( ph /\ ps /\ ch ) /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )

Proof

Step	Hyp	Ref	Expression
1		df-3an	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
2	1	anbi1i	|- ( ( ( ph /\ ps /\ ch ) /\ th ) <-> ( ( ( ph /\ ps ) /\ ch ) /\ th ) )
3		anass	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )
4	2 3	bitri	|- ( ( ( ph /\ ps /\ ch ) /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )