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Definition df-ltr 8565
 Description: Define ordering relation on signed reals. This is a "temporary" set used in the construction of complex numbers df-c 8623, 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.) (New usage is discouraged.)
Assertion
Ref Expression
df-ltr
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-ltr
StepHypRef Expression
1 cltr 8375 . 2
2 vx . . . . . . 7
32cv 1618 . . . . . 6
4 cnr 8369 . . . . . 6
53, 4wcel 1621 . . . . 5
6 vy . . . . . . 7
76cv 1618 . . . . . 6
87, 4wcel 1621 . . . . 5
95, 8wa 360 . . . 4
10 vz . . . . . . . . . . . . . 14
1110cv 1618 . . . . . . . . . . . . 13
12 vw . . . . . . . . . . . . . 14
1312cv 1618 . . . . . . . . . . . . 13
1411, 13cop 3547 . . . . . . . . . . . 12
15 cer 8368 . . . . . . . . . . . 12
1614, 15cec 6544 . . . . . . . . . . 11
173, 16wceq 1619 . . . . . . . . . 10
18 vv . . . . . . . . . . . . . 14
1918cv 1618 . . . . . . . . . . . . 13
20 vu . . . . . . . . . . . . . 14
2120cv 1618 . . . . . . . . . . . . 13
2219, 21cop 3547 . . . . . . . . . . . 12
2322, 15cec 6544 . . . . . . . . . . 11
247, 23wceq 1619 . . . . . . . . . 10
2517, 24wa 360 . . . . . . . . 9
26 cpp 8363 . . . . . . . . . . 11
2711, 21, 26co 5710 . . . . . . . . . 10
2813, 19, 26co 5710 . . . . . . . . . 10
29 cltp 8365 . . . . . . . . . 10
3027, 28, 29wbr 3920 . . . . . . . . 9
3125, 30wa 360 . . . . . . . 8
3231, 20wex 1537 . . . . . . 7
3332, 18wex 1537 . . . . . 6
3433, 12wex 1537 . . . . 5
3534, 10wex 1537 . . . 4
369, 35wa 360 . . 3
3736, 2, 6copab 3973 . 2
381, 37wceq 1619 1
 Colors of variables: wff set class This definition is referenced by:  ltrelsr  8573  ltsrpr  8579
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