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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 4872 shows that it doesn't matter which meaning we pick.) (Contributed by NM, 4-Nov-2002.) |
Ref | Expression |
---|---|
dffun7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun6 4859 |
. 2
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2 | moabs 1946 |
. . . . . 6
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3 | vex 2554 |
. . . . . . . 8
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4 | 3 | eldm 4475 |
. . . . . . 7
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5 | 4 | imbi1i 227 |
. . . . . 6
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6 | 2, 5 | bitr4i 176 |
. . . . 5
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7 | 6 | albii 1356 |
. . . 4
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8 | df-ral 2305 |
. . . 4
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9 | 7, 8 | bitr4i 176 |
. . 3
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10 | 9 | anbi2i 430 |
. 2
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11 | 1, 10 | bitri 173 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 df-opab 3810 df-id 4021 df-cnv 4296 df-co 4297 df-dm 4298 df-fun 4847 |
This theorem is referenced by: dffun8 4872 dffun9 4873 funco 4883 funimaexglem 4925 frecuzrdgfn 8879 |
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