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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 5300 | . 2 | |
2 | df-f1 5098 | . . 3 | |
3 | 2 | simprbi 273 | . 2 |
4 | f1orn 5345 | . 2 | |
5 | 1, 3, 4 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 ccnv 4508 crn 4510 wfun 5087 wfn 5088 wf 5089 wf1 5090 wf1o 5092 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 |
This theorem is referenced by: f1ores 5350 f1cnv 5359 f1cocnv1 5365 f1ocnvfvrneq 5651 ssenen 6713 f1dmvrnfibi 6800 |
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