Definition df-fo 4831

Description: Define an onto function. Definition 6.15(4) of [TakeutiZaring] p. 27. We use their notation ("onto" under the arrow). (Contributed by NM, 1-Aug-1994.)

Assertion

Ref	Expression
df-fo	⊢ (𝐹:A–onto→B ↔ (𝐹 Fn A ∧ ran 𝐹 = B))

Detailed syntax breakdown of Definition df-fo

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3		cF	. . 3 class 𝐹
4	1, 2, 3	wfo 4823	. 2 wff 𝐹:A–onto→B
5	3, 1	wfn 4820	. . 3 wff 𝐹 Fn A
6	3	crn 4269	. . . 4 class ran 𝐹
7	6, 2	wceq 1226	. . 3 wff ran 𝐹 = B
8	5, 7	wa 97	. 2 wff (𝐹 Fn A ∧ ran 𝐹 = B)
9	4, 8	wb 98	1 wff (𝐹:A–onto→B ↔ (𝐹 Fn A ∧ ran 𝐹 = B))

This definition is referenced by:  foeq1  5023  foeq2  5024  foeq3  5025  nffo  5026  fof  5027  forn  5030  dffo2  5031  dffn4  5033  fores  5036  dff1o2  5052  dff1o3  5053  foimacnv  5065  foun  5066  fconstfvm  5300  dff1o6  5337  fo1st  5703  fo2nd  5704  tposfo2  5800