| Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > df-funALTV | Structured version Visualization version GIF version | ||
| Description: Define the function
relation predicate, i.e., the function predicate.
This definition of the function predicate (based on a more general,
converse reflexive, relation) and the original definition of function in
set.mm df-fun 6563, are always the same, that is
( FunALTV 𝐹 ↔ Fun 𝐹), see funALTVfun 38699.
The element of the class of functions and the function predicate are the same, that is (𝐹 ∈ FunsALTV ↔ FunALTV 𝐹) when 𝐹 is a set, see elfunsALTVfunALTV 38698. Alternate definitions are dffunALTV2 38689, ... , dffunALTV5 38692. (Contributed by Peter Mazsa, 17-Jul-2021.) |
| Ref | Expression |
|---|---|
| df-funALTV | ⊢ ( FunALTV 𝐹 ↔ ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cF | . . 3 class 𝐹 | |
| 2 | 1 | wfunALTV 38213 | . 2 wff FunALTV 𝐹 |
| 3 | 1 | ccoss 38182 | . . . 4 class ≀ 𝐹 |
| 4 | 3 | wcnvrefrel 38191 | . . 3 wff CnvRefRel ≀ 𝐹 |
| 5 | 1 | wrel 5690 | . . 3 wff Rel 𝐹 |
| 6 | 4, 5 | wa 395 | . 2 wff ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹) |
| 7 | 2, 6 | wb 206 | 1 wff ( FunALTV 𝐹 ↔ ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹)) |
| Colors of variables: wff setvar class |
| This definition is referenced by: dffunALTV2 38689 elfunsALTVfunALTV 38698 funALTVfun 38699 dfdisjALTV 38714 |
| Copyright terms: Public domain | W3C validator |