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Theorem aibnbna 41394
Description: Given a implies b, (not b), there exists a proof for (not a). (Contributed by Jarvin Udandy, 1-Sep-2016.)
Hypotheses
Ref Expression
aibnbna.1 (𝜑𝜓)
aibnbna.2 ¬ 𝜓
Assertion
Ref Expression
aibnbna ¬ 𝜑

Proof of Theorem aibnbna
StepHypRef Expression
1 aibnbna.2 . 2 ¬ 𝜓
2 aibnbna.1 . 2 (𝜑𝜓)
31, 2mto 188 1 ¬ 𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  aibnbaif  41395
  Copyright terms: Public domain W3C validator