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Theorem dfor2 895
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 ((𝜑𝜓) ↔ ((𝜑𝜓) → 𝜓))

Proof of Theorem dfor2
StepHypRef Expression
1 pm2.62 893 . 2 ((𝜑𝜓) → ((𝜑𝜓) → 𝜓))
2 pm2.68 894 . 2 (((𝜑𝜓) → 𝜓) → (𝜑𝜓))
31, 2impbii 210 1 ((𝜑𝜓) ↔ ((𝜑𝜓) → 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wo 841
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 208  df-or 842
This theorem is referenced by:  imimorb  944  ifpim23g  39739
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