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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 6564, are always the same, that is
( FunALTV 𝐹 ↔ Fun 𝐹), see funALTVfun 38679.
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 38678. Alternate definitions are dffunALTV2 38669, ... , dffunALTV5 38672. (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 38192 | . 2 wff FunALTV 𝐹 |
3 | 1 | ccoss 38161 | . . . 4 class ≀ 𝐹 |
4 | 3 | wcnvrefrel 38170 | . . 3 wff CnvRefRel ≀ 𝐹 |
5 | 1 | wrel 5693 | . . 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 38669 elfunsALTVfunALTV 38678 funALTVfun 38679 dfdisjALTV 38694 |
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