![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 9891 | . 2 class inl | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cvv 3466 | . . 3 class V | |
4 | c0 4315 | . . . 4 class ∅ | |
5 | 2 | cv 1532 | . . . 4 class 𝑥 |
6 | 4, 5 | cop 4627 | . . 3 class ⟨∅, 𝑥⟩ |
7 | 2, 3, 6 | cmpt 5222 | . 2 class (𝑥 ∈ V ↦ ⟨∅, 𝑥⟩) |
8 | 1, 7 | wceq 1533 | 1 wff inl = (𝑥 ∈ V ↦ ⟨∅, 𝑥⟩) |
Colors of variables: wff setvar class |
This definition is referenced by: djulcl 9902 djulf1o 9904 inlresf 9906 djur 9911 djuss 9912 djuun 9918 1stinl 9919 2ndinl 9920 |
Copyright terms: Public domain | W3C validator |