Theorem 3anan12

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011) (Revised to shorten 3ancoma by Wolf Lammen, 5-Jun-2022.)

	Ref	Expression
Assertion	3anan12	|- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		3anass	|- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2		an12	|- ( ( ph /\ ( ps /\ ch ) ) <-> ( ps /\ ( ph /\ ch ) ) )
3	1 2	bitri	|- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )