Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nbfal | GIF version |
Description: The negation of a proposition is equivalent to itself being equivalent to ⊥. (Contributed by Anthony Hart, 14-Aug-2011.) |
Ref | Expression |
---|---|
nbfal | ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1291 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | nbn 647 | 1 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 103 ⊥wfal 1289 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 |
This theorem is referenced by: zfnuleu 3902 |
Copyright terms: Public domain | W3C validator |