Definition df-xr 8021

Description: Define the set of extended reals that includes plus and minus infinity. Definition 12-3.1 of [Gleason] p. 173. (Contributed by NM, 13-Oct-2005.)

Assertion

Ref	Expression
df-xr	|- RR* = ( RR u. { +oo , -oo } )

Detailed syntax breakdown of Definition df-xr

Step	Hyp	Ref	Expression
1		cxr 8016	. 2 class RR*
2		cr 7835	. . 3 class RR
3		cpnf 8014	. . . 4 class +oo
4		cmnf 8015	. . . 4 class -oo
5	3, 4	cpr 3608	. . 3 class { +oo , -oo }
6	2, 5	cun 3142	. 2 class ( RR u. { +oo , -oo } )
7	1, 6	wceq 1364	1 wff RR* = ( RR u. { +oo , -oo } )

This definition is referenced by:  ressxr  8026  pnfxr  8035  mnfxr  8039  ltrelxr  8043  elxr  9801  xrex  9881