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Definition df-ltxr 9176
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 9171 . 2
2 vx . . . . . . 7
32cv 1653 . . . . . 6
4 cr 9040 . . . . . 6
53, 4wcel 1728 . . . . 5
6 vy . . . . . . 7
76cv 1653 . . . . . 6
87, 4wcel 1728 . . . . 5
9 cltrr 9045 . . . . . 6
103, 7, 9wbr 4243 . . . . 5
115, 8, 10w3a 937 . . . 4
1211, 2, 6copab 4300 . . 3
13 cmnf 9169 . . . . . . 7
1413csn 3841 . . . . . 6
154, 14cun 3307 . . . . 5
16 cpnf 9168 . . . . . 6
1716csn 3841 . . . . 5
1815, 17cxp 4917 . . . 4
1914, 4cxp 4917 . . . 4
2018, 19cun 3307 . . 3
2112, 20cun 3307 . 2
221, 21wceq 1654 1
Colors of variables: wff set class
This definition is referenced by:  ltrelxr  9190  ltxrlt  9197  ltxr  10766
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