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Definition df-ltxr 6862
 Description: Define 'less than' on the set of extended reals. Definition 12-3.1 of [Gleason] p. 173. Note that in our postulates for complex numbers, is primitive and not necessarily a relation on . (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
df-ltxr
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-ltxr
StepHypRef Expression
1 clt 6857 . 2
2 vx . . . . . . 7
32cv 1241 . . . . . 6
4 cr 6710 . . . . . 6
53, 4wcel 1390 . . . . 5
6 vy . . . . . . 7
76cv 1241 . . . . . 6
87, 4wcel 1390 . . . . 5
9 cltrr 6715 . . . . . 6
103, 7, 9wbr 3755 . . . . 5
115, 8, 10w3a 884 . . . 4
1211, 2, 6copab 3808 . . 3
13 cmnf 6855 . . . . . . 7
1413csn 3367 . . . . . 6
154, 14cun 2909 . . . . 5
16 cpnf 6854 . . . . . 6
1716csn 3367 . . . . 5
1815, 17cxp 4286 . . . 4
1914, 4cxp 4286 . . . 4
2018, 19cun 2909 . . 3
2112, 20cun 2909 . 2
221, 21wceq 1242 1
 Colors of variables: wff set class This definition is referenced by:  ltrelxr  6877  ltxrlt  6882  ltxr  8465
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