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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-proj | Structured version Visualization version GIF version |
Description: Definition of the class projection corresponding to tagged tuples. The expression (𝐴 Proj 𝐵) denotes the projection on the A^th component. (Contributed by BJ, 6-Apr-2019.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-bj-proj | ⊢ (𝐴 Proj 𝐵) = {𝑥 ∣ {𝑥} ∈ (𝐵 “ {𝐴})} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | bj-cproj 34917 | . 2 class (𝐴 Proj 𝐵) |
4 | vx | . . . . . 6 setvar 𝑥 | |
5 | 4 | cv 1542 | . . . . 5 class 𝑥 |
6 | 5 | csn 4541 | . . . 4 class {𝑥} |
7 | 1 | csn 4541 | . . . . 5 class {𝐴} |
8 | 2, 7 | cima 5554 | . . . 4 class (𝐵 “ {𝐴}) |
9 | 6, 8 | wcel 2110 | . . 3 wff {𝑥} ∈ (𝐵 “ {𝐴}) |
10 | 9, 4 | cab 2714 | . 2 class {𝑥 ∣ {𝑥} ∈ (𝐵 “ {𝐴})} |
11 | 3, 10 | wceq 1543 | 1 wff (𝐴 Proj 𝐵) = {𝑥 ∣ {𝑥} ∈ (𝐵 “ {𝐴})} |
Colors of variables: wff setvar class |
This definition is referenced by: bj-projeq 34919 bj-projun 34921 bj-projex 34922 bj-projval 34923 |
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