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 〉 ) |