Theorem dfor2 400

Description: Logical 'or' expressed in terms of implication only. Theorem *5.25 of [WhiteheadRussell] p. 124. (Contributed by NM, 12-Aug-2004.) (Proof shortened by Wolf Lammen, 20-Oct-2012.)

Assertion

Ref	Expression
dfor2	|- ((ph \/ ps) <-> ((ph -> ps) -> ps))

Proof of Theorem dfor2

Step	Hyp	Ref	Expression
1		pm2.62 398	. 2 |- ((ph \/ ps) -> ((ph -> ps) -> ps))
2		pm2.68 399	. 2 |- (((ph -> ps) -> ps) -> (ph \/ ps))
3	1, 2	impbii 180	1 |- ((ph \/ ps) <-> ((ph -> ps) -> ps))

Syntax hints:   -> 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:  imimorb  847