Theorem dfor2 229

Description: Logical 'or' expressed in terms of implication only. Theorem *5.25 of [WhiteheadRussell] p. 124.

Assertion

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

Proof of Theorem dfor2

Step	Hyp	Ref	Expression
1		df-or 224	. 2 |- ((ph \/ ps) <-> (-. ph -> ps))
2		pm2.6 133	. . 3 |- ((-. ph -> ps) -> ((ph -> ps) -> ps))
3		pm2.21 76	. . . 4 |- (-. ph -> (ph -> ps))
4	3	imim1i 16	. . 3 |- (((ph -> ps) -> ps) -> (-. ph -> ps))
5	2, 4	impbii 157	. 2 |- ((-. ph -> ps) <-> ((ph -> ps) -> ps))
6	1, 5	bitri 173	1 |- ((ph \/ ps) <-> ((ph -> ps) -> ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222

This theorem is referenced by:  pm2.62 248  pm2.68 250

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224

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