Theorem pm5.7 746

Description: Disjunction distributes over the biconditional. Theorem *5.7 of [WhiteheadRussell] p. 125. This theorem is similar to orbidi 743. (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 743	. 2 |- ((ch \/ (ph <-> ps)) <-> ((ch \/ ph) <-> (ch \/ ps)))
2		orcom 246	. . 3 |- ((ch \/ ph) <-> (ph \/ ch))
3		orcom 246	. . 3 |- ((ch \/ ps) <-> (ps \/ ch))
4	2, 3	bibi12i 610	. 2 |- (((ch \/ ph) <-> (ch \/ ps)) <-> ((ph \/ ch) <-> (ps \/ ch)))
5	1, 4	bitr2 174	1 |- (((ph \/ ch) <-> (ps \/ ch)) <-> (ch \/ (ph <-> ps)))

Syntax hints:   <-> wb 146   \/ wo 222

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

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