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Theorem atbiffatnnb 41825
Description: If a implies b, then a implies not not b. (Contributed by Jarvin Udandy, 28-Aug-2016.)
Assertion
Ref Expression
atbiffatnnb ((𝜑𝜓) → (𝜑 → ¬ ¬ 𝜓))

Proof of Theorem atbiffatnnb
StepHypRef Expression
1 idd 24 . . 3 (𝜑 → (𝜓𝜓))
2 notnotb 307 . . 3 (𝜓 ↔ ¬ ¬ 𝜓)
31, 2syl6ib 243 . 2 (𝜑 → (𝜓 → ¬ ¬ 𝜓))
43a2i 14 1 ((𝜑𝜓) → (𝜑 → ¬ ¬ 𝜓))
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 depends on definitions:  df-bi 199
This theorem is referenced by:  atbiffatnnbalt  41827
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