Theorem pm5.6

Description: Conjunction in antecedent versus disjunction in consequent. Theorem *5.6 of WhiteheadRussell p. 125. (Contributed by NM, 8-Jun-1994)

	Ref	Expression
Assertion	pm5.6	|- ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( ps \/ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		impexp	|- ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( -. ps -> ch ) ) )
2		df-or	|- ( ( ps \/ ch ) <-> ( -. ps -> ch ) )
3	2	imbi2i	|- ( ( ph -> ( ps \/ ch ) ) <-> ( ph -> ( -. ps -> ch ) ) )
4	1 3	bitr4i	|- ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( ps \/ ch ) ) )