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Mirrors > Home > ILE Home > Th. List > dfrnf | Unicode version |
Description: Definition of range, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 14-Aug-1995.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
dfrnf.1 |
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dfrnf.2 |
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Ref | Expression |
---|---|
dfrnf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfrn2 4655 |
. 2
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2 | nfcv 2235 |
. . . . 5
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3 | dfrnf.1 |
. . . . 5
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4 | nfcv 2235 |
. . . . 5
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5 | 2, 3, 4 | nfbr 3911 |
. . . 4
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6 | nfv 1473 |
. . . 4
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7 | breq1 3870 |
. . . 4
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8 | 5, 6, 7 | cbvex 1693 |
. . 3
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9 | 8 | abbii 2210 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | nfcv 2235 |
. . . . 5
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11 | dfrnf.2 |
. . . . 5
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12 | nfcv 2235 |
. . . . 5
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13 | 10, 11, 12 | nfbr 3911 |
. . . 4
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14 | 13 | nfex 1580 |
. . 3
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15 | nfv 1473 |
. . 3
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16 | breq2 3871 |
. . . 4
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17 | 16 | exbidv 1760 |
. . 3
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18 | 14, 15, 17 | cbvab 2217 |
. 2
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19 | 1, 9, 18 | 3eqtri 2119 |
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 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-v 2635 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-br 3868 df-opab 3922 df-cnv 4475 df-dm 4477 df-rn 4478 |
This theorem is referenced by: rnopab 4714 |
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