Theorem pm5.7 900

Description: Disjunction distributes over the biconditional. Theorem *5.7 of [WhiteheadRussell] p. 125. This theorem is similar to orbidi 898. (Contributed by Roy F. Longton, 21-Jun-2005.)

Assertion

Ref	Expression
pm5.7	|- (((ph \/ ch) <-> (ps \/ ch)) <-> (ch \/ (ph <-> ps)))

Proof of Theorem pm5.7

Step	Hyp	Ref	Expression
1		orbidi 898	. 2 |- ((ch \/ (ph <-> ps)) <-> ((ch \/ ph) <-> (ch \/ ps)))
2		orcom 376	. . 3 |- ((ch \/ ph) <-> (ph \/ ch))
3		orcom 376	. . 3 |- ((ch \/ ps) <-> (ps \/ ch))
4	2, 3	bibi12i 306	. 2 |- (((ch \/ ph) <-> (ch \/ ps)) <-> ((ph \/ ch) <-> (ps \/ ch)))
5	1, 4	bitr2i 241	1 |- (((ph \/ ch) <-> (ps \/ ch)) <-> (ch \/ (ph <-> ps)))

Syntax hints:   <-> wb 176   \/ wo 357

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

This theorem is referenced by: (None)