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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 5263 shows that it does not matter which meaning we pick.) (Contributed by NM, 4-Nov-2002.) |
Ref | Expression |
---|---|
dffun7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun6 5249 |
. 2
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2 | moabs 2087 |
. . . . . 6
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3 | vex 2755 |
. . . . . . . 8
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4 | 3 | eldm 4842 |
. . . . . . 7
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5 | 4 | imbi1i 238 |
. . . . . 6
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6 | 2, 5 | bitr4i 187 |
. . . . 5
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7 | 6 | albii 1481 |
. . . 4
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8 | df-ral 2473 |
. . . 4
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9 | 7, 8 | bitr4i 187 |
. . 3
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10 | 9 | anbi2i 457 |
. 2
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11 | 1, 10 | bitri 184 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-id 4311 df-cnv 4652 df-co 4653 df-dm 4654 df-fun 5237 |
This theorem is referenced by: dffun8 5263 dffun9 5264 funco 5275 funimaexglem 5318 frecuzrdgtcl 10443 frecuzrdgfunlem 10450 imasaddfnlemg 12791 |
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