Definition df-mnf 11298

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 11304 and pnfnemnf 11316). (Contributed by NM, 13-Oct-2005.) (New usage is discouraged.)

Assertion

Ref	Expression
df-mnf	⊢ -∞ = 𝒫 +∞

Detailed syntax breakdown of Definition df-mnf

Step	Hyp	Ref	Expression
1		cmnf 11293	. 2 class -∞
2		cpnf 11292	. . 3 class +∞
3	2	cpw 4600	. 2 class 𝒫 +∞
4	1, 3	wceq 1540	1 wff -∞ = 𝒫 +∞

This definition is referenced by:  mnfnre  11304  pnfnemnf  11316  mnfxr  11318