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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]]"). (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.) |
Ref | Expression |
---|---|
falim | ⊢ (⊥ → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1637 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | pm2.21i 116 | 1 ⊢ (⊥ → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊥wfal 1635 |
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 197 df-tru 1633 df-fal 1636 |
This theorem is referenced by: falimd 1646 falimtru 1663 tbw-bijust 1770 tbw-negdf 1771 tbw-ax4 1775 merco1 1785 merco2 1808 csbprc 4121 csbprcOLD 4122 ralnralall 4222 tgcgr4 25623 frgrregord013 27561 nalf 32706 imsym1 32721 consym1 32723 dissym1 32724 unisym1 32726 exisym1 32727 bj-falor2 32874 orfa1 34197 orfa2 34198 bifald 34199 botel 34217 lindslinindsimp2 42760 |
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