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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 9328 | . 2 class inl | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cvv 3494 | . . 3 class V | |
4 | c0 4291 | . . . 4 class ∅ | |
5 | 2 | cv 1536 | . . . 4 class 𝑥 |
6 | 4, 5 | cop 4573 | . . 3 class 〈∅, 𝑥〉 |
7 | 2, 3, 6 | cmpt 5146 | . 2 class (𝑥 ∈ V ↦ 〈∅, 𝑥〉) |
8 | 1, 7 | wceq 1537 | 1 wff inl = (𝑥 ∈ V ↦ 〈∅, 𝑥〉) |
Colors of variables: wff setvar class |
This definition is referenced by: djulcl 9339 djulf1o 9341 inlresf 9343 djur 9348 djuss 9349 djuun 9355 1stinl 9356 2ndinl 9357 |
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