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Mirrors > Home > ILE Home > Th. List > dffun7 | Unicode version |
Description: Alternate definition of a function. One possibility for the definition of a function in [Enderton] p. 42. (Enderton's definition is ambiguous because "there is only one" could mean either "there is at most one" or "there is exactly one." However, dffun8 4949 shows that it doesn't matter which meaning we pick.) (Contributed by NM, 4-Nov-2002.) |
Ref | Expression |
---|---|
dffun7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun6 4936 | . 2 | |
2 | moabs 1990 | . . . . . 6 | |
3 | vex 2604 | . . . . . . . 8 | |
4 | 3 | eldm 4550 | . . . . . . 7 |
5 | 4 | imbi1i 236 | . . . . . 6 |
6 | 2, 5 | bitr4i 185 | . . . . 5 |
7 | 6 | albii 1399 | . . . 4 |
8 | df-ral 2353 | . . . 4 | |
9 | 7, 8 | bitr4i 185 | . . 3 |
10 | 9 | anbi2i 444 | . 2 |
11 | 1, 10 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wex 1421 wcel 1433 wmo 1942 wral 2348 class class class wbr 3785 cdm 4363 wrel 4368 wfun 4916 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-id 4048 df-cnv 4371 df-co 4372 df-dm 4373 df-fun 4924 |
This theorem is referenced by: dffun8 4949 dffun9 4950 funco 4960 funimaexglem 5002 frecuzrdgfn 9414 |
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