Theorem dfor2 246

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 241	. 2 |- ((ph \/ ps) <-> (-. ph -> ps))
2		pm2.6 148	. . 3 |- ((-. ph -> ps) -> ((ph -> ps) -> ps))
3		pm2.21 92	. . . 4 |- (-. ph -> (ph -> ps))
4	3	imim1i 19	. . 3 |- (((ph -> ps) -> ps) -> (-. ph -> ps))
5	2, 4	impbii 174	. 2 |- ((-. ph -> ps) <-> ((ph -> ps) -> ps))
6	1, 5	bitri 190	1 |- ((ph \/ ps) <-> ((ph -> ps) -> ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 163   \/ wo 239

This theorem is referenced by:  pm2.62 268  pm2.68 270

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 164  df-or 241

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