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Theorem rb-imdf 1713
 Description: The definition of implication, in terms of ∨ and ¬. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rb-imdf ¬ (¬ (¬ (𝜑𝜓) ∨ (¬ 𝜑𝜓)) ∨ ¬ (¬ (¬ 𝜑𝜓) ∨ (𝜑𝜓)))

Proof of Theorem rb-imdf
StepHypRef Expression
1 imor 839 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
2 rb-bijust 1712 . 2 (((𝜑𝜓) ↔ (¬ 𝜑𝜓)) ↔ ¬ (¬ (¬ (𝜑𝜓) ∨ (¬ 𝜑𝜓)) ∨ ¬ (¬ (¬ 𝜑𝜓) ∨ (𝜑𝜓))))
31, 2mpbi 222 1 ¬ (¬ (¬ (𝜑𝜓) ∨ (¬ 𝜑𝜓)) ∨ ¬ (¬ (¬ 𝜑𝜓) ∨ (𝜑𝜓)))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 198   ∨ wo 833 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 199  df-or 834 This theorem is referenced by:  re1axmp  1727  re2luk1  1728  re2luk2  1729  re2luk3  1730
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