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Metamath Proof Explorer

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	$⊢ +_{𝑵} = {+_{𝑜} ↾}_{(𝑵 \times 𝑵)}$

Detailed syntax breakdown

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