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Mirrors > Home > ILE Home > Th. List > f1f1orn | Unicode version |
Description: A one-to-one function maps one-to-one onto its range. (Contributed by NM, 4-Sep-2004.) |
Ref | Expression |
---|---|
f1f1orn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 5124 |
. 2
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2 | df-f1 4937 |
. . 3
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3 | 2 | simprbi 269 |
. 2
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4 | f1orn 5167 |
. 2
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5 | 1, 3, 4 | sylanbrc 408 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-11 1438 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-in 2980 df-ss 2987 df-f 4936 df-f1 4937 df-fo 4938 df-f1o 4939 |
This theorem is referenced by: f1ores 5172 f1cnv 5181 f1cocnv1 5187 f1ocnvfvrneq 5453 f1dmvrnfibi 6452 |
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