Theorem ordir 453

Description: Distributive law for disjunction.

Assertion

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

Proof of Theorem ordir

Step	Hyp	Ref	Expression
1		ordi 452	. 2 |- ((ch \/ (ph /\ ps)) <-> ((ch \/ ph) /\ (ch \/ ps)))
2		orcom 209	. 2 |- (((ph /\ ps) \/ ch) <-> (ch \/ (ph /\ ps)))
3		orcom 209	. . 3 |- ((ph \/ ch) <-> (ch \/ ph))
4		orcom 209	. . 3 |- ((ps \/ ch) <-> (ch \/ ps))
5	3, 4	anbi12i 369	. 2 |- (((ph \/ ch) /\ (ps \/ ch)) <-> ((ch \/ ph) /\ (ch \/ ps)))
6	1, 2, 5	3bitr4 158	1 |- (((ph /\ ps) \/ ch) <-> ((ph \/ ch) /\ (ps \/ ch)))

Syntax hints:   <-> wb 127   \/ wo 195   /\ wa 196

This theorem is referenced by:  orddi 458  mapdom2 3389  elnn0z 4574

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

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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