Definition df-ltnq

Description: Define ordering relation on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c , 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
Assertion	df-ltnq	$$⊢{<}_{𝑸}={<}_{\mathrm{𝑝𝑸}}\cap \left(𝑸\times 𝑸\right)$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cltq	$$class{<}_{𝑸}$$
1		cltpq	$$class{<}_{\mathrm{𝑝𝑸}}$$
2		cnq	$$class𝑸$$
3	2 2	cxp	$$class\left(𝑸\times 𝑸\right)$$
4	1 3	cin	$$class\left({<}_{\mathrm{𝑝𝑸}}\cap \left(𝑸\times 𝑸\right)\right)$$
5	0 4	wceq	$$wff{<}_{𝑸}={<}_{\mathrm{𝑝𝑸}}\cap \left(𝑸\times 𝑸\right)$$