Definition df-xr 8328

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 8323	. 2 class RR*
2		cr 8142	. . 3 class RR
3		cpnf 8321	. . . 4 class +oo
4		cmnf 8322	. . . 4 class -oo
5	3, 4	cpr 3695	. . 3 class { +oo , -oo }
6	2, 5	cun 3212	. 2 class ( RR u. { +oo , -oo } )
7	1, 6	wceq 1398	1 wff RR* = ( RR u. { +oo , -oo } )

This definition is referenced by:  ressxr  8333  pnfxr  8342  mnfxr  8346  ltrelxr  8350  elxr  10128  xrex  10208