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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 5146 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 5132 | . 2 | |
2 | moabs 2046 | . . . . . 6 | |
3 | vex 2684 | . . . . . . . 8 | |
4 | 3 | eldm 4731 | . . . . . . 7 |
5 | 4 | imbi1i 237 | . . . . . 6 |
6 | 2, 5 | bitr4i 186 | . . . . 5 |
7 | 6 | albii 1446 | . . . 4 |
8 | df-ral 2419 | . . . 4 | |
9 | 7, 8 | bitr4i 186 | . . 3 |
10 | 9 | anbi2i 452 | . 2 |
11 | 1, 10 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wex 1468 wcel 1480 wmo 1998 wral 2414 class class class wbr 3924 cdm 4534 wrel 4539 wfun 5112 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-id 4210 df-cnv 4542 df-co 4543 df-dm 4544 df-fun 5120 |
This theorem is referenced by: dffun8 5146 dffun9 5147 funco 5158 funimaexglem 5201 frecuzrdgtcl 10178 frecuzrdgfunlem 10185 |
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