Definition df-shs 31294

Description: Define subspace sum in S_ℋ. See shsval 31298, shsval2i 31373, and shsval3i 31374 for its value. (Contributed by NM, 16-Oct-1999.) (New usage is discouraged.)

Assertion

Ref	Expression
df-shs	⊢ +ℋ = (𝑥 ∈ Sℋ , 𝑦 ∈ Sℋ ↦ ( +ℎ “ (𝑥 × 𝑦)))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-shs

Step	Hyp	Ref	Expression
1		cph 30917	. 2 class +ℋ
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		csh 30914	. . 3 class Sℋ
5		cva 30906	. . . 4 class +ℎ
6	2	cv 1539	. . . . 5 class 𝑥
7	3	cv 1539	. . . . 5 class 𝑦
8	6, 7	cxp 5657	. . . 4 class (𝑥 × 𝑦)
9	5, 8	cima 5662	. . 3 class ( +ℎ “ (𝑥 × 𝑦))
10	2, 3, 4, 4, 9	cmpo 7412	. 2 class (𝑥 ∈ Sℋ , 𝑦 ∈ Sℋ ↦ ( +ℎ “ (𝑥 × 𝑦)))
11	1, 10	wceq 1540	1 wff +ℋ = (𝑥 ∈ Sℋ , 𝑦 ∈ Sℋ ↦ ( +ℎ “ (𝑥 × 𝑦)))

This definition is referenced by:  shsval  31298