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Definition df-ltr 7644
 Description: Define ordering relation on signed reals. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. From Proposition 9-4.4 of [Gleason] p. 127. (Contributed by NM, 14-Feb-1996.)
Assertion
Ref Expression
df-ltr
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-ltr
StepHypRef Expression
1 cltr 7217 . 2
2 vx . . . . . . 7
32cv 1334 . . . . . 6
4 cnr 7211 . . . . . 6
53, 4wcel 2128 . . . . 5
6 vy . . . . . . 7
76cv 1334 . . . . . 6
87, 4wcel 2128 . . . . 5
95, 8wa 103 . . . 4
10 vz . . . . . . . . . . . . . 14
1110cv 1334 . . . . . . . . . . . . 13
12 vw . . . . . . . . . . . . . 14
1312cv 1334 . . . . . . . . . . . . 13
1411, 13cop 3563 . . . . . . . . . . . 12
15 cer 7210 . . . . . . . . . . . 12
1614, 15cec 6475 . . . . . . . . . . 11
173, 16wceq 1335 . . . . . . . . . 10
18 vv . . . . . . . . . . . . . 14
1918cv 1334 . . . . . . . . . . . . 13
20 vu . . . . . . . . . . . . . 14
2120cv 1334 . . . . . . . . . . . . 13
2219, 21cop 3563 . . . . . . . . . . . 12
2322, 15cec 6475 . . . . . . . . . . 11
247, 23wceq 1335 . . . . . . . . . 10
2517, 24wa 103 . . . . . . . . 9
26 cpp 7207 . . . . . . . . . . 11
2711, 21, 26co 5821 . . . . . . . . . 10
2813, 19, 26co 5821 . . . . . . . . . 10
29 cltp 7209 . . . . . . . . . 10
3027, 28, 29wbr 3965 . . . . . . . . 9
3125, 30wa 103 . . . . . . . 8
3231, 20wex 1472 . . . . . . 7
3332, 18wex 1472 . . . . . 6
3433, 12wex 1472 . . . . 5
3534, 10wex 1472 . . . 4
369, 35wa 103 . . 3
3736, 2, 6copab 4024 . 2
381, 37wceq 1335 1
 Colors of variables: wff set class This definition is referenced by:  ltrelsr  7652  ltsrprg  7661
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