Description: Left injection of a disjoint union. (Contributed by Mario Carneiro, 21-Jun-2022)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-inl | |- inl = ( x e. _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 e. _V |-> <. (/) , x >. ) | 
| 7 | 0 6 | wceq | |- inl = ( x e. _V |-> <. (/) , x >. ) |