Definition df-cda 9213

Description: Define cardinal number addition. Definition of cardinal sum in [Mendelson] p. 258. See cdaval 9215 for its value and a description. (Contributed by NM, 24-Sep-2004.)

Assertion

Ref	Expression
df-cda	⊢ +𝑐 = (𝑥 ∈ V, 𝑦 ∈ V ↦ ((𝑥 × {∅}) ∪ (𝑦 × {1𝑜})))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-cda

Step	Hyp	Ref	Expression
1		ccda 9212	. 2 class +𝑐
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cvv 3355	. . 3 class V
5	2	cv 1633	. . . . 5 class 𝑥
6		c0 4073	. . . . . 6 class ∅
7	6	csn 4326	. . . . 5 class {∅}
8	5, 7	cxp 5261	. . . 4 class (𝑥 × {∅})
9	3	cv 1633	. . . . 5 class 𝑦
10		c1o 7727	. . . . . 6 class 1𝑜
11	10	csn 4326	. . . . 5 class {1𝑜}
12	9, 11	cxp 5261	. . . 4 class (𝑦 × {1𝑜})
13	8, 12	cun 3727	. . 3 class ((𝑥 × {∅}) ∪ (𝑦 × {1𝑜}))
14	2, 3, 4, 4, 13	cmpt2 6814	. 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ ((𝑥 × {∅}) ∪ (𝑦 × {1𝑜})))
15	1, 14	wceq 1634	1 wff +𝑐 = (𝑥 ∈ V, 𝑦 ∈ V ↦ ((𝑥 × {∅}) ∪ (𝑦 × {1𝑜})))

This definition is referenced by:  cdafn  9214  cdaval  9215