Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bnj14 | Structured version Visualization version GIF version |
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 |
---|---|
df-bnj14 | ⊢ pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋} |
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 32379 | . 2 class pred(𝑋, 𝐴, 𝑅) |
5 | vy | . . . . 5 setvar 𝑦 | |
6 | 5 | cv 1542 | . . . 4 class 𝑦 |
7 | 6, 3, 2 | wbr 5053 | . . 3 wff 𝑦𝑅𝑋 |
8 | 7, 5, 1 | crab 3065 | . 2 class {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋} |
9 | 4, 8 | wceq 1543 | 1 wff pred(𝑋, 𝐴, 𝑅) = {𝑦 ∈ 𝐴 ∣ 𝑦𝑅𝑋} |
Colors of variables: wff setvar class |
This definition is referenced by: bnj213 32575 bnj602 32608 bnj1152 32691 bnj1279 32711 bnj1418 32733 |
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