Theorem orimdi

Description: Disjunction distributes over implication. (Contributed by Wolf Lammen, 5-Jan-2013)

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

Proof

Step	Hyp	Ref	Expression
1		imdi	|- ( ( -. ph -> ( ps -> ch ) ) <-> ( ( -. ph -> ps ) -> ( -. ph -> ch ) ) )
2		df-or	|- ( ( ph \/ ( ps -> ch ) ) <-> ( -. ph -> ( ps -> ch ) ) )
3		df-or	|- ( ( ph \/ ps ) <-> ( -. ph -> ps ) )
4		df-or	|- ( ( ph \/ ch ) <-> ( -. ph -> ch ) )
5	3 4	imbi12i	|- ( ( ( ph \/ ps ) -> ( ph \/ ch ) ) <-> ( ( -. ph -> ps ) -> ( -. ph -> ch ) ) )
6	1 2 5	3bitr4i	|- ( ( ph \/ ( ps -> ch ) ) <-> ( ( ph \/ ps ) -> ( ph \/ ch ) ) )