Theorem orimdi 820

Description: Disjunction distributes over implication. (Contributed by Wolf Lammen, 5-Jan-2013.)

Assertion

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

Proof of Theorem orimdi

Step	Hyp	Ref	Expression
1		imdi 352	. 2 |- ((-. ph -> (ps -> ch)) <-> ((-. ph -> ps) -> (-. ph -> ch)))
2		df-or 359	. 2 |- ((ph \/ (ps -> ch)) <-> (-. ph -> (ps -> ch)))
3		df-or 359	. . 3 |- ((ph \/ ps) <-> (-. ph -> ps))
4		df-or 359	. . 3 |- ((ph \/ ch) <-> (-. ph -> ch))
5	3, 4	imbi12i 316	. 2 |- (((ph \/ ps) -> (ph \/ ch)) <-> ((-. ph -> ps) -> (-. ph -> ch)))
6	1, 2, 5	3bitr4i 268	1 |- ((ph \/ (ps -> ch)) <-> ((ph \/ ps) -> (ph \/ ch)))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  pm2.76  821  pm2.85  826