Theorem pm5.54

Description: Theorem *5.54 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 7-Nov-2013)

	Ref	Expression
Assertion	pm5.54	|- ( ( ( ph /\ ps ) <-> ph ) \/ ( ( ph /\ ps ) <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		iba	|- ( ps -> ( ph <-> ( ph /\ ps ) ) )
2	1	bicomd	|- ( ps -> ( ( ph /\ ps ) <-> ph ) )
3	2	adantl	|- ( ( ph /\ ps ) -> ( ( ph /\ ps ) <-> ph ) )
4	3 2	pm5.21ni	|- ( -. ( ( ph /\ ps ) <-> ph ) -> ( ( ph /\ ps ) <-> ps ) )
5	4	orri	|- ( ( ( ph /\ ps ) <-> ph ) \/ ( ( ph /\ ps ) <-> ps ) )