Theorem orbidi 973

Description: Disjunction distributes over the biconditional. An axiom of system DS in Vladimir Lifschitz, "On calculational proofs" (1998), http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.3384. (Contributed by NM, 8-Jan-2005.) (Proof shortened by Wolf Lammen, 4-Feb-2013.)

Assertion

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

Proof of Theorem orbidi

Step	Hyp	Ref	Expression
1		pm5.74 259	. 2 |- ( ( -. ph -> ( ps <-> ch ) ) <-> ( ( -. ph -> ps ) <-> ( -. ph -> ch ) ) )
2		df-or 385	. 2 |- ( ( ph \/ ( ps <-> ch ) ) <-> ( -. ph -> ( ps <-> ch ) ) )
3		df-or 385	. . 3 |- ( ( ph \/ ps ) <-> ( -. ph -> ps ) )
4		df-or 385	. . 3 |- ( ( ph \/ ch ) <-> ( -. ph -> ch ) )
5	3, 4	bibi12i 329	. 2 |- ( ( ( ph \/ ps ) <-> ( ph \/ ch ) ) <-> ( ( -. ph -> ps ) <-> ( -. ph -> ch ) ) )
6	1, 2, 5	3bitr4i 292	1 |- ( ( ph \/ ( ps <-> ch ) ) <-> ( ( ph \/ ps ) <-> ( ph \/ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383

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 197  df-or 385

This theorem is referenced by:  pm5.7  975