Definition df-fo 4908

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 4900	. 2 wff 𝐹:𝐴–onto→𝐵
5	3, 1	wfn 4897	. . 3 wff 𝐹 Fn 𝐴
6	3	crn 4346	. . . 4 class ran 𝐹
7	6, 2	wceq 1243	. . 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  5102  foeq2  5103  foeq3  5104  nffo  5105  fof  5106  forn  5109  dffo2  5110  dffn4  5112  fores  5115  dff1o2  5131  dff1o3  5132  foimacnv  5144  foun  5145  fconstfvm  5379  dff1o6  5416  fo1st  5784  fo2nd  5785  tposfo2  5882