Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > df-inl | 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 6938 | . 2 class inl | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cvv 2689 | . . 3 class V | |
4 | c0 3368 | . . . 4 class ∅ | |
5 | 2 | cv 1331 | . . . 4 class 𝑥 |
6 | 4, 5 | cop 3535 | . . 3 class 〈∅, 𝑥〉 |
7 | 2, 3, 6 | cmpt 3997 | . 2 class (𝑥 ∈ V ↦ 〈∅, 𝑥〉) |
8 | 1, 7 | wceq 1332 | 1 wff inl = (𝑥 ∈ V ↦ 〈∅, 𝑥〉) |
Colors of variables: wff set class |
This definition is referenced by: djulclr 6942 djulcl 6944 djulclb 6948 djulf1or 6949 djulf1o 6951 inl11 6958 djuss 6963 1stinl 6967 2ndinl 6968 caseinj 6982 caseinl 6984 djudoml 7092 djulclALT 13179 |
Copyright terms: Public domain | W3C validator |