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| Mirrors > Home > MPE Home > Th. List > df-inl | Structured version Visualization version GIF version | ||
| Description: Left injection of a disjoint union. (Contributed by Mario Carneiro, 21-Jun-2022.) |
| Ref | Expression |
|---|---|
| df-inl | ⊢ inl = (𝑥 ∈ V ↦ 〈∅, 𝑥〉) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cinl 9939 | . 2 class inl | |
| 2 | vx | . . 3 setvar 𝑥 | |
| 3 | cvv 3480 | . . 3 class V | |
| 4 | c0 4333 | . . . 4 class ∅ | |
| 5 | 2 | cv 1539 | . . . 4 class 𝑥 |
| 6 | 4, 5 | cop 4632 | . . 3 class 〈∅, 𝑥〉 |
| 7 | 2, 3, 6 | cmpt 5225 | . 2 class (𝑥 ∈ V ↦ 〈∅, 𝑥〉) |
| 8 | 1, 7 | wceq 1540 | 1 wff inl = (𝑥 ∈ V ↦ 〈∅, 𝑥〉) |
| Colors of variables: wff setvar class |
| This definition is referenced by: djulcl 9950 djulf1o 9952 inlresf 9954 djur 9959 djuss 9960 djuun 9966 1stinl 9967 2ndinl 9968 |
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