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Definition df-f1o 5225
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 5217 . 2 wff 𝐹:𝐴1-1-onto𝐵
51, 2, 3wf1 5215 . . 3 wff 𝐹:𝐴1-1𝐵
61, 2, 3wfo 5216 . . 3 wff 𝐹:𝐴onto𝐵
75, 6wa 104 . 2 wff (𝐹:𝐴1-1𝐵𝐹:𝐴onto𝐵)
84, 7wb 105 1 wff (𝐹:𝐴1-1-onto𝐵 ↔ (𝐹:𝐴1-1𝐵𝐹:𝐴onto𝐵))
Colors of variables: wff set class
This definition is referenced by:  f1oeq1  5451  f1oeq2  5452  f1oeq3  5453  nff1o  5461  f1of1  5462  dff1o2  5468  dff1o5  5472  f1oco  5486  fo00  5499  dff1o6  5780  fcof1o  5793  tposf1o2  6274  cnref1o  9653  1arith  12368  xpsff1o  12774  reeff1o  14334  ioocosf1o  14415
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