Definition df-fo

Description: Define an onto function. Definition 6.15(4) of TakeutiZaring p. 27. We use their notation ("onto" under the arrow). For alternate definitions, see dffo2 , dffo3 , dffo4 , and dffo5 .

An onto function is also called a "surjection" or a "surjective function", F : A -onto-> B can be read as " F is a surjection from A onto B ". Surjections are precisely the epimorphisms in the category SetCat of sets and set functions, see setcepi . (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Assertion	df-fo	|- ( F : A -onto-> B <-> ( F Fn A /\ ran F = B ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cF	|- F
1		cA	|- A
2		cB	|- B
3	1 2 0	wfo	|- F : A -onto-> B
4	0 1	wfn	|- F Fn A
5	0	crn	|- ran F
6	5 2	wceq	|- ran F = B
7	4 6	wa	|- ( F Fn A /\ ran F = B )
8	3 7	wb	|- ( F : A -onto-> B <-> ( F Fn A /\ ran F = B ) )