Definition df-bnj14 34703

Description: Define the function giving: the class of all elements of 𝐴 that are "smaller" than 𝑋 according to 𝑅. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
df-bnj14	⊢ pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋}

Distinct variable groups:   𝑦,𝑋   𝑦,𝐴   𝑦,𝑅

Detailed syntax breakdown of Definition df-bnj14

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cR	. . 3 class 𝑅
3		cX	. . 3 class 𝑋
4	1, 2, 3	c-bnj14 34702	. 2 class pred(𝑋, 𝐴, 𝑅)
5		vy	. . . . 5 setvar 𝑦
6	5	cv 1539	. . . 4 class 𝑦
7	6, 3, 2	wbr 5143	. . 3 wff 𝑦𝑅𝑋
8	7, 5, 1	crab 3436	. 2 class {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋}
9	4, 8	wceq 1540	1 wff pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋}

This definition is referenced by:  bnj213  34896  bnj602  34929  bnj1152  35012  bnj1279  35032  bnj1418  35054