Definition df-bnj14

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.)

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

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cX	⊢ 𝑋
1		cA	⊢ 𝐴
2		cR	⊢ 𝑅
3	1 2 0	c-bnj14	⊢ pred ( 𝑋 , 𝐴 , 𝑅 )
4		vy	⊢ 𝑦
5	4	cv	⊢ 𝑦
6	5 0 2	wbr	⊢ 𝑦 𝑅 𝑋
7	6 4 1	crab	⊢ { 𝑦 ∈ 𝐴 ∣ 𝑦 𝑅 𝑋 }
8	3 7	wceq	⊢ pred ( 𝑋 , 𝐴 , 𝑅 ) = { 𝑦 ∈ 𝐴 ∣ 𝑦 𝑅 𝑋 }