Theorem pm4.78 565

Description: Theorem *4.78 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)

Assertion

Ref	Expression
pm4.78	|- (((ph -> ps) \/ (ph -> ch)) <-> (ph -> (ps \/ ch)))

Proof of Theorem pm4.78

Step	Hyp	Ref	Expression
1		orordi 516	. 2 |- ((-. ph \/ (ps \/ ch)) <-> ((-. ph \/ ps) \/ (-. ph \/ ch)))
2		imor 401	. 2 |- ((ph -> (ps \/ ch)) <-> (-. ph \/ (ps \/ ch)))
3		imor 401	. . 3 |- ((ph -> ps) <-> (-. ph \/ ps))
4		imor 401	. . 3 |- ((ph -> ch) <-> (-. ph \/ ch))
5	3, 4	orbi12i 507	. 2 |- (((ph -> ps) \/ (ph -> ch)) <-> ((-. ph \/ ps) \/ (-. ph \/ ch)))
6	1, 2, 5	3bitr4ri 269	1 |- (((ph -> ps) \/ (ph -> ch)) <-> (ph -> (ps \/ ch)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357

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 177  df-or 359

This theorem is referenced by: (None)