Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-staf | Structured version Visualization version GIF version |
Description: Define the functionalization of the involution in a star ring. This is not strictly necessary but by having *𝑟 as an actual function we can state the principal properties of an involution much more cleanly. (Contributed by Mario Carneiro, 6-Oct-2015.) |
Ref | Expression |
---|---|
df-staf | ⊢ *rf = (𝑓 ∈ V ↦ (𝑥 ∈ (Base‘𝑓) ↦ ((*𝑟‘𝑓)‘𝑥))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cstf 19726 | . 2 class *rf | |
2 | vf | . . 3 setvar 𝑓 | |
3 | cvv 3397 | . . 3 class V | |
4 | vx | . . . 4 setvar 𝑥 | |
5 | 2 | cv 1541 | . . . . 5 class 𝑓 |
6 | cbs 16579 | . . . . 5 class Base | |
7 | 5, 6 | cfv 6333 | . . . 4 class (Base‘𝑓) |
8 | 4 | cv 1541 | . . . . 5 class 𝑥 |
9 | cstv 16663 | . . . . . 6 class *𝑟 | |
10 | 5, 9 | cfv 6333 | . . . . 5 class (*𝑟‘𝑓) |
11 | 8, 10 | cfv 6333 | . . . 4 class ((*𝑟‘𝑓)‘𝑥) |
12 | 4, 7, 11 | cmpt 5107 | . . 3 class (𝑥 ∈ (Base‘𝑓) ↦ ((*𝑟‘𝑓)‘𝑥)) |
13 | 2, 3, 12 | cmpt 5107 | . 2 class (𝑓 ∈ V ↦ (𝑥 ∈ (Base‘𝑓) ↦ ((*𝑟‘𝑓)‘𝑥))) |
14 | 1, 13 | wceq 1542 | 1 wff *rf = (𝑓 ∈ V ↦ (𝑥 ∈ (Base‘𝑓) ↦ ((*𝑟‘𝑓)‘𝑥))) |
Colors of variables: wff setvar class |
This definition is referenced by: staffval 19730 |
Copyright terms: Public domain | W3C validator |