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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 1486 | . 2 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥)) | |
3 | 1, 2 | mpbir 220 | 1 ⊢ ¬ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 ⊥wfal 1480 |
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 df-tru 1478 df-fal 1481 |
This theorem is referenced by: aistbisfiaxb 39735 aisfbistiaxb 39736 aifftbifffaibif 39737 aifftbifffaibifff 39738 atnaiana 39739 dandysum2p2e4 39814 |
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