Definition df-pli

Description: Define addition 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-pli	$$⊢{+}_{𝑵}={{+}_{𝑜}\upharpoonright }_{\left(𝑵\times 𝑵\right)}$$

Detailed syntax breakdown

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