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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-fset | Structured version Visualization version GIF version |
Description: Define the set of functions between two sets. Same as df-map 7746 with arguments swapped. TODO: prove the same staple lemmas as for ↑𝑚. (Contributed by BJ, 11-Apr-2020.) |
Ref | Expression |
---|---|
df-bj-fset | ⊢ Set⟶ = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑥⟶𝑦}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfset 32256 | . 2 class Set⟶ | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . 3 setvar 𝑦 | |
4 | cvv 3173 | . . 3 class V | |
5 | 2 | cv 1474 | . . . . 5 class 𝑥 |
6 | 3 | cv 1474 | . . . . 5 class 𝑦 |
7 | vf | . . . . . 6 setvar 𝑓 | |
8 | 7 | cv 1474 | . . . . 5 class 𝑓 |
9 | 5, 6, 8 | wf 5800 | . . . 4 wff 𝑓:𝑥⟶𝑦 |
10 | 9, 7 | cab 2596 | . . 3 class {𝑓 ∣ 𝑓:𝑥⟶𝑦} |
11 | 2, 3, 4, 4, 10 | cmpt2 6551 | . 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑥⟶𝑦}) |
12 | 1, 11 | wceq 1475 | 1 wff Set⟶ = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑥⟶𝑦}) |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
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