Definition df-xr 8357

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 8352	. 2 class RR*
2		cr 8171	. . 3 class RR
3		cpnf 8350	. . . 4 class +oo
4		cmnf 8351	. . . 4 class -oo
5	3, 4	cpr 3709	. . 3 class { +oo , -oo }
6	2, 5	cun 3218	. 2 class ( RR u. { +oo , -oo } )
7	1, 6	wceq 1402	1 wff RR* = ( RR u. { +oo , -oo } )

This definition is referenced by:  ressxr  8362  pnfxr  8371  mnfxr  8375  ltrelxr  8379  elxr  10160  xrex  10240