Theorem pm5.6 878

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

Assertion

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

Proof of Theorem pm5.6

Step	Hyp	Ref	Expression
1		impexp 433	. 2 |- (((ph /\ -. ps) -> ch) <-> (ph -> (-. ps -> ch)))
2		df-or 359	. . 3 |- ((ps \/ ch) <-> (-. ps -> ch))
3	2	imbi2i 303	. 2 |- ((ph -> (ps \/ ch)) <-> (ph -> (-. ps -> ch)))
4	1, 3	bitr4i 243	1 |- (((ph /\ -. ps) -> ch) <-> (ph -> (ps \/ ch)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by:  ssundif  3634