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Mirrors > Home > MPE Home > Th. List > Mathboxes > atbiffatnnbalt | Structured version Visualization version GIF version |
Description: If a implies b, then a implies not not b. (Contributed by Jarvin Udandy, 29-Aug-2016.) |
Ref | Expression |
---|---|
atbiffatnnbalt | ⊢ ((𝜑 → 𝜓) → (𝜑 → ¬ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | atbiffatnnb 44375 | 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 206 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |