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Theorem rb-imdf 1515
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) φ ψ)) ¬ (¬ (¬ φ ψ) (φψ)))

Proof of Theorem rb-imdf
StepHypRef Expression
1 imor 401 . 2 ((φψ) ↔ (¬ φ ψ))
2 rb-bijust 1514 . 2 (((φψ) ↔ (¬ φ ψ)) ↔ ¬ (¬ (¬ (φψ) φ ψ)) ¬ (¬ (¬ φ ψ) (φψ))))
31, 2mpbi 199 1 ¬ (¬ (¬ (φψ) φ ψ)) ¬ (¬ (¬ φ ψ) (φψ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wo 357
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 177  df-or 359
This theorem is referenced by:  re1axmp  1529  re2luk1  1530  re2luk2  1531  re2luk3  1532
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