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Definition df-f1o 4825
Description: Define a one-to-one onto function. Compare Definition 6.15(6) of [TakeutiZaring] p. 27. We use their notation ("1-1" above the arrow and "onto" below the arrow). (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-f1o (𝐹:A1-1-ontoB ↔ (𝐹:A1-1B 𝐹:AontoB))

Detailed syntax breakdown of Definition df-f1o
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
3 cF . . 3 class 𝐹
41, 2, 3wf1o 4817 . 2 wff 𝐹:A1-1-ontoB
51, 2, 3wf1 4815 . . 3 wff 𝐹:A1-1B
61, 2, 3wfo 4816 . . 3 wff 𝐹:AontoB
75, 6wa 97 . 2 wff (𝐹:A1-1B 𝐹:AontoB)
84, 7wb 98 1 wff (𝐹:A1-1-ontoB ↔ (𝐹:A1-1B 𝐹:AontoB))
Colors of variables: wff set class
This definition is referenced by:  f1oeq1  5031  f1oeq2  5032  f1oeq3  5033  nff1o  5038  f1of1  5039  dff1o2  5045  dff1o5  5049  f1oco  5063  fo00  5076  dff1o6  5330  fcof1o  5343  tposf1o2  5796
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