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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 5056 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 5042 |
. 2
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2 | moabs 1998 |
. . . . . 6
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3 | vex 2623 |
. . . . . . . 8
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4 | 3 | eldm 4646 |
. . . . . . 7
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5 | 4 | imbi1i 237 |
. . . . . 6
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6 | 2, 5 | bitr4i 186 |
. . . . 5
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7 | 6 | albii 1405 |
. . . 4
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8 | df-ral 2365 |
. . . 4
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9 | 7, 8 | bitr4i 186 |
. . 3
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10 | 9 | anbi2i 446 |
. 2
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11 | 1, 10 | bitri 183 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 df-opab 3906 df-id 4129 df-cnv 4460 df-co 4461 df-dm 4462 df-fun 5030 |
This theorem is referenced by: dffun8 5056 dffun9 5057 funco 5067 funimaexglem 5110 frecuzrdgtcl 9880 frecuzrdgfunlem 9887 |
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