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Definition df-bnj14 29802
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) = {𝑦𝐴𝑦𝑅𝑋}
Distinct variable groups:   𝑦,𝑋   𝑦,𝐴   𝑦,𝑅

Detailed syntax breakdown of Definition df-bnj14
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cR . . 3 class 𝑅
3 cX . . 3 class 𝑋
41, 2, 3c-bnj14 29801 . 2 class pred(𝑋, 𝐴, 𝑅)
5 vy . . . . 5 setvar 𝑦
65cv 1474 . . . 4 class 𝑦
76, 3, 2wbr 4578 . . 3 wff 𝑦𝑅𝑋
87, 5, 1crab 2900 . 2 class {𝑦𝐴𝑦𝑅𝑋}
94, 8wceq 1475 1 wff pred(𝑋, 𝐴, 𝑅) = {𝑦𝐴𝑦𝑅𝑋}
Colors of variables: wff setvar class
This definition is referenced by:  bnj213  30000  bnj602  30033  bnj1152  30114  bnj1279  30134  bnj1418  30156
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