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Definition df-f1o 5130
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:𝐴1-1𝐵𝐹: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 5122 . 2 wff 𝐹:𝐴1-1-onto𝐵
51, 2, 3wf1 5120 . . 3 wff 𝐹:𝐴1-1𝐵
61, 2, 3wfo 5121 . . 3 wff 𝐹:𝐴onto𝐵
75, 6wa 103 . 2 wff (𝐹:𝐴1-1𝐵𝐹:𝐴onto𝐵)
84, 7wb 104 1 wff (𝐹:𝐴1-1-onto𝐵 ↔ (𝐹:𝐴1-1𝐵𝐹:𝐴onto𝐵))
Colors of variables: wff set class
This definition is referenced by:  f1oeq1  5356  f1oeq2  5357  f1oeq3  5358  nff1o  5365  f1of1  5366  dff1o2  5372  dff1o5  5376  f1oco  5390  fo00  5403  dff1o6  5677  fcof1o  5690  tposf1o2  6167  cnref1o  9452  reeff1o  12877  ioocosf1o  12957
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