Definition df-lec 6100

Description: Define cardinal less than or equal. Definition from [Rosser] p. 375. (Contributed by Scott Fenton, 24-Feb-2015.)

Assertion

Ref	Expression
df-lec	⊢ ≤c = {⟨a, b⟩ ∣ ∃x ∈ a ∃y ∈ b x ⊆ y}

Distinct variable group:   x,y,a,b

Detailed syntax breakdown of Definition df-lec

Step	Hyp	Ref	Expression
1		clec 6090	. 2 class ≤c
2		vx	. . . . . . 7 setvar x
3	2	cv 1641	. . . . . 6 class x
4		vy	. . . . . . 7 setvar y
5	4	cv 1641	. . . . . 6 class y
6	3, 5	wss 3258	. . . . 5 wff x ⊆ y
7		vb	. . . . . 6 setvar b
8	7	cv 1641	. . . . 5 class b
9	6, 4, 8	wrex 2616	. . . 4 wff ∃y ∈ b x ⊆ y
10		va	. . . . 5 setvar a
11	10	cv 1641	. . . 4 class a
12	9, 2, 11	wrex 2616	. . 3 wff ∃x ∈ a ∃y ∈ b x ⊆ y
13	12, 10, 7	copab 4623	. 2 class {⟨a, b⟩ ∣ ∃x ∈ a ∃y ∈ b x ⊆ y}
14	1, 13	wceq 1642	1 wff ≤c = {⟨a, b⟩ ∣ ∃x ∈ a ∃y ∈ b x ⊆ y}

This definition is referenced by:  brlecg  6113