Definition df-funALTV 37540

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 6542, are always the same, that is ( FunALTV 𝐹 ↔ Fun 𝐹), see funALTVfun 37556.

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 37555. Alternate definitions are dffunALTV2 37546, ... , dffunALTV5 37549. (Contributed by Peter Mazsa, 17-Jul-2021.)

Assertion

Ref	Expression
df-funALTV	⊢ ( FunALTV 𝐹 ↔ ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹))

Detailed syntax breakdown of Definition df-funALTV

Step	Hyp	Ref	Expression
1		cF	. . 3 class 𝐹
2	1	wfunALTV 37062	. 2 wff FunALTV 𝐹
3	1	ccoss 37031	. . . 4 class ≀ 𝐹
4	3	wcnvrefrel 37040	. . 3 wff CnvRefRel ≀ 𝐹
5	1	wrel 5680	. . 3 wff Rel 𝐹
6	4, 5	wa 396	. 2 wff ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹)
7	2, 6	wb 205	1 wff ( FunALTV 𝐹 ↔ ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹))

This definition is referenced by:  dffunALTV2  37546  elfunsALTVfunALTV  37555  funALTVfun  37556  dfdisjALTV  37571