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Mirrors > Home > MPE Home > Th. List > Mathboxes > aisfina | Structured version Visualization version GIF version |
Description: Given a is equivalent to ⊥, there exists a proof for not a. (Contributed by Jarvin Udandy, 30-Aug-2016.) |
Ref | Expression |
---|---|
aisfina.1 | ⊢ (𝜑 ↔ ⊥) |
Ref | Expression |
---|---|
aisfina | ⊢ ¬ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aisfina.1 | . 2 ⊢ (𝜑 ↔ ⊥) | |
2 | nbfal 1557 | . 2 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥)) | |
3 | 1, 2 | mpbir 234 | 1 ⊢ ¬ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ⊥wfal 1554 |
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 210 df-tru 1545 df-fal 1555 |
This theorem is referenced by: aistbisfiaxb 43975 aisfbistiaxb 43976 aifftbifffaibif 43977 aifftbifffaibifff 43978 atnaiana 43979 dandysum2p2e4 44054 |
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