Definition df-cross 5765

Description: Define the cross product function. (Contributed by SF, 9-Feb-2015.)

Assertion

Ref	Expression
df-cross	⊢ Cross = (x ∈ V, y ∈ V ↦ (x × y))

Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-cross

Step	Hyp	Ref	Expression
1		ccross 5764	. 2 class Cross
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cvv 2860	. . 3 class V
5	2	cv 1641	. . . 4 class x
6	3	cv 1641	. . . 4 class y
7	5, 6	cxp 4771	. . 3 class (x × y)
8	2, 3, 4, 4, 7	cmpt2 5654	. 2 class (x ∈ V, y ∈ V ↦ (x × y))
9	1, 8	wceq 1642	1 wff Cross = (x ∈ V, y ∈ V ↦ (x × y))

This definition is referenced by:  ovcross  5846  fncross  5847  crossex  5851