Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 1482 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | pm2.21i 115 | 1 ⊢ (⊥ → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊥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: falimd 1490 falimtru 1507 tbw-bijust 1614 tbw-negdf 1615 tbw-ax4 1619 merco1 1629 merco2 1652 csbprc 3932 csbprcOLD 3933 tgcgr4 25226 frgrareg 26644 frgraregord013 26645 nalf 31572 imsym1 31587 consym1 31589 dissym1 31590 unisym1 31592 exisym1 31593 bj-falor2 31743 orfa1 33056 orfa2 33057 bifald 33058 botel 33076 ralnralall 40307 av-frgraregord013 41549 lindslinindsimp2 42046 |
Copyright terms: Public domain | W3C validator |