![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > df-mnf | GIF version |
Description: Define minus infinity as the power set of plus infinity. Note that the definition is arbitrary, requiring only that -∞ be a set not in ℝ and different from +∞ (see mnfnre 8031). (Contributed by NM, 13-Oct-2005.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-mnf | ⊢ -∞ = 𝒫 +∞ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmnf 8021 | . 2 class -∞ | |
2 | cpnf 8020 | . . 3 class +∞ | |
3 | 2 | cpw 3590 | . 2 class 𝒫 +∞ |
4 | 1, 3 | wceq 1364 | 1 wff -∞ = 𝒫 +∞ |
Colors of variables: wff set class |
This definition is referenced by: mnfnre 8031 pnfnemnf 8043 mnfxr 8045 |
Copyright terms: Public domain | W3C validator |