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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 4929 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 4916 |
. 2
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2 | moabs 1949 |
. . . . . 6
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3 | vex 2560 |
. . . . . . . 8
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4 | 3 | eldm 4532 |
. . . . . . 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 1359 |
. . . 4
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8 | df-ral 2311 |
. . . 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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-id 4030 df-cnv 4353 df-co 4354 df-dm 4355 df-fun 4904 |
This theorem is referenced by: dffun8 4929 dffun9 4930 funco 4940 funimaexglem 4982 frecuzrdgfn 9198 |
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