Definition df-f1 4885

Description: Define a one-to-one function. Compare Definition 6.15(5) of [TakeutiZaring] p. 27. We use their notation ("1-1" above the arrow). (Contributed by NM, 1-Aug-1994.)

Assertion

Ref	Expression
df-f1	|- ( F : A -1-1-> B <-> ( F : A --> B /\ Fun `' F ) )

Detailed syntax breakdown of Definition df-f1

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3		cF	. . 3 class F
4	1, 2, 3	wf1 4877	. 2 wff F : A -1-1-> B
5	1, 2, 3	wf 4876	. . 3 wff F : A --> B
6	3	ccnv 4322	. . . 4 class `' F
7	6	wfun 4874	. . 3 wff Fun `' F
8	5, 7	wa 97	. 2 wff ( F : A --> B /\ Fun `' F )
9	4, 8	wb 98	1 wff ( F : A -1-1-> B <-> ( F : A --> B /\ Fun `' F ) )

This definition is referenced by:  f1eq1  5065  f1eq2  5066  f1eq3  5067  nff1  5068  dff12  5069  f1f  5070  f1ss  5075  f1ssr  5076  f1ssres  5077  f1cnvcnv  5078  f1co  5079  dff1o2  5109  f1f1orn  5115  f1imacnv  5121  fun11iun  5125  f11o  5137  f10  5138  f1o2ndf1  5827  ssdomg  6236  phplem4dom  6302