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Mirrors > Home > ILE Home > Th. List > fodmrnu | Unicode version |
Description: An onto function has unique domain and range. (Contributed by NM, 5-Nov-2006.) |
Ref | Expression |
---|---|
fodmrnu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fofn 5406 | . . 3 | |
2 | fofn 5406 | . . 3 | |
3 | fndmu 5283 | . . 3 | |
4 | 1, 2, 3 | syl2an 287 | . 2 |
5 | forn 5407 | . . 3 | |
6 | forn 5407 | . . 3 | |
7 | 5, 6 | sylan9req 2218 | . 2 |
8 | 4, 7 | jca 304 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 crn 4599 wfn 5177 wfo 5180 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3117 df-ss 3124 df-fn 5185 df-f 5186 df-fo 5188 |
This theorem is referenced by: (None) |
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