Definition df-mnf 10870

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 10876 and pnfnemnf 10888). (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 10865	. 2 class -∞
2		cpnf 10864	. . 3 class +∞
3	2	cpw 4513	. 2 class 𝒫 +∞
4	1, 3	wceq 1543	1 wff -∞ = 𝒫 +∞

This definition is referenced by:  mnfnre  10876  pnfnemnf  10888  mnfxr  10890