Definition df-mi

Description: Define multiplication on positive integers. This is a "temporary" set used in the construction of complex numbers df-c , and is intended to be used only by the construction. (Contributed by NM, 26-Aug-1995) (New usage is discouraged.)

	Ref	Expression
Assertion	df-mi	$$⊢{\cdot }_{𝑵}={{\cdot }_{𝑜}\upharpoonright }_{\left(𝑵\times 𝑵\right)}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cmi	$$class{\cdot }_{𝑵}$$
1		comu	$$class{\cdot }_{𝑜}$$
2		cnpi	$$class𝑵$$
3	2 2	cxp	$$class\left(𝑵\times 𝑵\right)$$
4	1 3	cres	$$class\left({{\cdot }_{𝑜}\upharpoonright }_{\left(𝑵\times 𝑵\right)}\right)$$
5	0 4	wceq	$$wff{\cdot }_{𝑵}={{\cdot }_{𝑜}\upharpoonright }_{\left(𝑵\times 𝑵\right)}$$