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Definition df-funALTV 35459
 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 6230, are always the same, that is ( FunALTV 𝐹 ↔ Fun 𝐹), see funALTVfun 35475. 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 35474. Alternate definitions are dffunALTV2 35465, ... , dffunALTV5 35468. (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
StepHypRef Expression
1 cF . . 3 class 𝐹
21wfunALTV 35029 . 2 wff FunALTV 𝐹
31ccoss 34998 . . . 4 class 𝐹
43wcnvrefrel 35007 . . 3 wff CnvRefRel ≀ 𝐹
51wrel 5451 . . 3 wff Rel 𝐹
64, 5wa 396 . 2 wff ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹)
72, 6wb 207 1 wff ( FunALTV 𝐹 ↔ ( CnvRefRel ≀ 𝐹 ∧ Rel 𝐹))
 Colors of variables: wff setvar class This definition is referenced by:  dffunALTV2  35465  elfunsALTVfunALTV  35474  funALTVfun  35475  dfdisjALTV  35490
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