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Theorem imnot 340
 Description: If a proposition is false, then implying it is equivalent to being false. One of four theorems that can be used to simplify an implication , the other ones being ax-1 6 (true consequent), pm2.21 108 (false antecedent), pm5.5 336 (true antecedent). (Contributed by Mario Carneiro, 26-Apr-2019.) (Proof shortened by Wolf Lammen, 26-May-2019.)
Assertion
Ref Expression
imnot

Proof of Theorem imnot
StepHypRef Expression
1 mtt 339 . 2
21bicomd 201 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184 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 185
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