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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 9840 | . 2 class inl | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cvv 3444 | . . 3 class V | |
4 | c0 4283 | . . . 4 class ∅ | |
5 | 2 | cv 1541 | . . . 4 class 𝑥 |
6 | 4, 5 | cop 4593 | . . 3 class ⟨∅, 𝑥⟩ |
7 | 2, 3, 6 | cmpt 5189 | . 2 class (𝑥 ∈ V ↦ ⟨∅, 𝑥⟩) |
8 | 1, 7 | wceq 1542 | 1 wff inl = (𝑥 ∈ V ↦ ⟨∅, 𝑥⟩) |
Colors of variables: wff setvar class |
This definition is referenced by: djulcl 9851 djulf1o 9853 inlresf 9855 djur 9860 djuss 9861 djuun 9867 1stinl 9868 2ndinl 9869 |
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