Description: Left injection of a disjoint union. (Contributed by Mario Carneiro, 21-Jun-2022)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-inl | ⊢ inl = ( 𝑥 ∈ V ↦ 〈 ∅ , 𝑥 〉 ) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 0 | cinl | ⊢ inl | |
| 1 | vx | ⊢ 𝑥 | |
| 2 | cvv | ⊢ V | |
| 3 | c0 | ⊢ ∅ | |
| 4 | 1 | cv | ⊢ 𝑥 | 
| 5 | 3 4 | cop | ⊢ 〈 ∅ , 𝑥 〉 | 
| 6 | 1 2 5 | cmpt | ⊢ ( 𝑥 ∈ V ↦ 〈 ∅ , 𝑥 〉 ) | 
| 7 | 0 6 | wceq | ⊢ inl = ( 𝑥 ∈ V ↦ 〈 ∅ , 𝑥 〉 ) |