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Mirrors > Home > MPE Home > Th. List > falim | Structured version Visualization version GIF version |
Description: The truth value ⊥ implies anything. Also called the "principle of explosion", or "ex falso [sequitur]] quodlibet" (Latin for "from falsehood, anything [follows]]"). Dual statement of trud 1538. (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.) |
Ref | Expression |
---|---|
falim | ⊢ (⊥ → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1542 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | pm2.21i 119 | 1 ⊢ (⊥ → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊥wfal 1540 |
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 208 df-tru 1531 df-fal 1541 |
This theorem is referenced by: falimd 1546 tbw-bijust 1690 tbw-negdf 1691 tbw-ax4 1695 merco1 1705 merco2 1728 csbprc 4357 ralnralall 4456 tgcgr4 26245 frgrregord013 28102 nalfal 33649 imsym1 33664 consym1 33666 dissym1 33667 unisym1 33669 exisym1 33670 bj-falor2 33817 orfa1 35246 orfa2 35247 bifald 35248 botel 35265 lindslinindsimp2 44416 |
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