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Theorem pm5.21im 365
Description: Two propositions are equivalent if they are both false. Closed form of 2false 366. Equivalent to a biimpr 211-like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013.)
Assertion
Ref Expression
pm5.21im 𝜑 → (¬ 𝜓 → (𝜑𝜓)))

Proof of Theorem pm5.21im
StepHypRef Expression
1 nbn2 361 . 2 𝜑 → (¬ 𝜓 ↔ (𝜑𝜓)))
21biimpd 220 1 𝜑 → (¬ 𝜓 → (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 197
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 198
This theorem is referenced by:  pm5.21ndd  370  pm5.21  855
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