Theorem imdistan

Description: Distribution of implication with conjunction. (Contributed by NM, 31-May-1999) (Proof shortened by Wolf Lammen, 6-Dec-2012)

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

Proof

Step	Hyp	Ref	Expression
1		pm5.42	|- ( ( ph -> ( ps -> ch ) ) <-> ( ph -> ( ps -> ( ph /\ ch ) ) ) )
2		impexp	|- ( ( ( ph /\ ps ) -> ( ph /\ ch ) ) <-> ( ph -> ( ps -> ( ph /\ ch ) ) ) )
3	1 2	bitr4i	|- ( ( ph -> ( ps -> ch ) ) <-> ( ( ph /\ ps ) -> ( ph /\ ch ) ) )