Theorem dfor2 427

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		pm2.62 425	. 2 |- ( ( ph \/ ps ) -> ( ( ph -> ps ) -> ps ) )
2		pm2.68 426	. 2 |- ( ( ( ph -> ps ) -> ps ) -> ( ph \/ ps ) )
3	1, 2	impbii 199	1 |- ( ( ph \/ ps ) <-> ( ( ph -> ps ) -> ps ) )

Syntax hints:   -> 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:  imimorb  921  ifpim23g  37840