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Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > atbiffatnnb | Structured version Visualization version GIF version |
Description: If a implies b, then a implies not not b. (Contributed by Jarvin Udandy, 28-Aug-2016.) |
Ref | Expression |
---|---|
atbiffatnnb | ⊢ ((𝜑 → 𝜓) → (𝜑 → ¬ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd 24 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜓)) | |
2 | notnotb 303 | . . 3 ⊢ (𝜓 ↔ ¬ ¬ 𝜓) | |
3 | 1, 2 | syl6ib 240 | . 2 ⊢ (𝜑 → (𝜓 → ¬ ¬ 𝜓)) |
4 | 3 | a2i 14 | 1 ⊢ ((𝜑 → 𝜓) → (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 196 |
This theorem is referenced by: atbiffatnnbalt 39730 |
Copyright terms: Public domain | W3C validator |