Theorem pm5.7 942

Description: Disjunction distributes over the biconditional. Theorem *5.7 of [WhiteheadRussell] p. 125. This theorem is similar to orbidi 940. (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 940	. 2 |- ( ( ch \/ ( ph <-> ps ) ) <-> ( ( ch \/ ph ) <-> ( ch \/ ps ) ) )
2		orcom 388	. . 3 |- ( ( ch \/ ph ) <-> ( ph \/ ch ) )
3		orcom 388	. . 3 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
4	2, 3	bibi12i 316	. 2 |- ( ( ( ch \/ ph ) <-> ( ch \/ ps ) ) <-> ( ( ph \/ ch ) <-> ( ps \/ ch ) ) )
5	1, 4	bitr2i 253	1 |- ( ( ( ph \/ ch ) <-> ( ps \/ ch ) ) <-> ( ch \/ ( ph <-> ps ) ) )

Syntax hints:   <-> wb 187   \/ wo 369

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 188  df-or 371

This theorem is referenced by: (None)