Theorem an31

Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012) (Proof shortened by Wolf Lammen, 31-Dec-2012)

	Ref	Expression
Assertion	an31	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ch /\ ps ) /\ ph ) )

Proof

Step	Hyp	Ref	Expression
1		an13	|- ( ( ph /\ ( ps /\ ch ) ) <-> ( ch /\ ( ps /\ ph ) ) )
2		anass	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		anass	|- ( ( ( ch /\ ps ) /\ ph ) <-> ( ch /\ ( ps /\ ph ) ) )
4	1 2 3	3bitr4i	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ch /\ ps ) /\ ph ) )