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Mirrors > Home > ILE Home > Th. List > ffdm | Unicode version |
Description: A mapping is a partial function. (Contributed by NM, 25-Nov-2007.) |
Ref | Expression |
---|---|
ffdm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fdm 5324 | . . . 4 | |
2 | 1 | feq2d 5306 | . . 3 |
3 | 2 | ibir 176 | . 2 |
4 | eqimss 3182 | . . 3 | |
5 | 1, 4 | syl 14 | . 2 |
6 | 3, 5 | jca 304 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wss 3102 cdm 4585 wf 5165 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-ss 3115 df-fn 5172 df-f 5173 |
This theorem is referenced by: smoiso 6246 dvcj 13060 dvfre 13061 |
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