MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-mnf Structured version   Visualization version   GIF version

Definition df-mnf 10279
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 and different from +∞ (see mnfnre 10284 and pnfnemnf 10296). (Contributed by NM, 13-Oct-2005.) (New usage is discouraged.)
Assertion
Ref Expression
df-mnf -∞ = 𝒫 +∞

Detailed syntax breakdown of Definition df-mnf
StepHypRef Expression
1 cmnf 10274 . 2 class -∞
2 cpnf 10273 . . 3 class +∞
32cpw 4297 . 2 class 𝒫 +∞
41, 3wceq 1631 1 wff -∞ = 𝒫 +∞
Colors of variables: wff setvar class
This definition is referenced by:  mnfnre  10284  pnfnemnf  10296  mnfxr  10298
  Copyright terms: Public domain W3C validator