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

Step	Hyp	Ref	Expression
1		mtt 339	. 2
2	1	bicomd 201	1

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