Metamath Proof Explorer


Theorem falim

Description: The truth value F. implies anything. Also called the "principle of explosion", or "ex falso [sequitur] quodlibet" (Latin for "from falsehood, anything [follows]"). Dual statement of trud . (Contributed by FL, 20-Mar-2011) (Proof shortened by Anthony Hart, 1-Aug-2011)

Ref Expression
Assertion falim φ

Proof

Step Hyp Ref Expression
1 fal ¬
2 1 pm2.21i φ