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Mirrors > Home > MPE Home > Th. List > df-ltnq | Structured version Visualization version GIF version |
Description: Define ordering relation on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c 10759, and is intended to be used only by the construction. Similar to Definition 5 of [Suppes] p. 162. (Contributed by NM, 13-Feb-1996.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-ltnq | ⊢ <Q = ( <pQ ∩ (Q × Q)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cltq 10496 | . 2 class <Q | |
2 | cltpq 10488 | . . 3 class <pQ | |
3 | cnq 10490 | . . . 4 class Q | |
4 | 3, 3 | cxp 5563 | . . 3 class (Q × Q) |
5 | 2, 4 | cin 3879 | . 2 class ( <pQ ∩ (Q × Q)) |
6 | 1, 5 | wceq 1543 | 1 wff <Q = ( <pQ ∩ (Q × Q)) |
Colors of variables: wff setvar class |
This definition is referenced by: ltrelnq 10564 ordpinq 10581 |
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