![]() |
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 9937 | . 2 class inl | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cvv 3478 | . . 3 class V | |
4 | c0 4339 | . . . 4 class ∅ | |
5 | 2 | cv 1536 | . . . 4 class 𝑥 |
6 | 4, 5 | cop 4637 | . . 3 class 〈∅, 𝑥〉 |
7 | 2, 3, 6 | cmpt 5231 | . 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 9948 djulf1o 9950 inlresf 9952 djur 9957 djuss 9958 djuun 9964 1stinl 9965 2ndinl 9966 |
Copyright terms: Public domain | W3C validator |