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Mirrors > Home > ILE Home > Th. List > dffun6f | Unicode version |
Description: Definition of function, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
dffun6f.1 |
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dffun6f.2 |
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Ref | Expression |
---|---|
dffun6f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun2 4855 |
. 2
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2 | nfcv 2175 |
. . . . . . 7
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3 | dffun6f.2 |
. . . . . . 7
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4 | nfcv 2175 |
. . . . . . 7
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5 | 2, 3, 4 | nfbr 3799 |
. . . . . 6
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6 | nfv 1418 |
. . . . . 6
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7 | breq2 3759 |
. . . . . 6
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8 | 5, 6, 7 | cbvmo 1937 |
. . . . 5
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9 | 8 | albii 1356 |
. . . 4
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10 | breq2 3759 |
. . . . . 6
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11 | 10 | mo4 1958 |
. . . . 5
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12 | 11 | albii 1356 |
. . . 4
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13 | nfcv 2175 |
. . . . . . 7
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14 | dffun6f.1 |
. . . . . . 7
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15 | nfcv 2175 |
. . . . . . 7
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16 | 13, 14, 15 | nfbr 3799 |
. . . . . 6
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17 | 16 | nfmo 1917 |
. . . . 5
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18 | nfv 1418 |
. . . . 5
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19 | breq1 3758 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 19 | mobidv 1933 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 17, 18, 20 | cbval 1634 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 9, 12, 21 | 3bitr3ri 200 |
. . 3
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23 | 22 | anbi2i 430 |
. 2
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24 | 1, 23 | bitr4i 176 |
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-fun 4847 |
This theorem is referenced by: dffun6 4859 dffun4f 4861 funopab 4878 |
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