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Metamath Proof Explorer

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	$⊢ <_{𝑸} = <_{𝑝𝑸} \cap (𝑸 \times 𝑸)$

Detailed syntax breakdown

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