Definition df-xr 7157

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 7152	. 2 class RR*
2		cr 6980	. . 3 class RR
3		cpnf 7150	. . . 4 class +oo
4		cmnf 7151	. . . 4 class -oo
5	3, 4	cpr 3399	. . 3 class { +oo , -oo }
6	2, 5	cun 2971	. 2 class ( RR u. { +oo , -oo } )
7	1, 6	wceq 1284	1 wff RR* = ( RR u. { +oo , -oo } )

This definition is referenced by:  ressxr  7162  ltrelxr  7173  pnfxr  8846  mnfxr  8848  elxr  8850  xrex  8910