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Mirrors > Home > MPE Home > Th. List > dfdm2 | Structured version Unicode version |
Description: Alternate definition of domain df-dm 4959 that doesn't require dummy variables. (Contributed by NM, 2-Aug-2010.) |
Ref | Expression |
---|---|
dfdm2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvco 5134 |
. . . . . 6
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2 | cocnvcnv2 5458 |
. . . . . 6
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3 | 1, 2 | eqtri 2483 |
. . . . 5
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4 | 3 | unieqi 4209 |
. . . 4
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5 | 4 | unieqi 4209 |
. . 3
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6 | unidmrn 5476 |
. . 3
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7 | 5, 6 | eqtr3i 2485 |
. 2
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8 | df-rn 4960 |
. . . . 5
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9 | 8 | eqcomi 2467 |
. . . 4
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10 | dmcoeq 5211 |
. . . 4
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11 | 9, 10 | ax-mp 5 |
. . 3
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12 | rncoeq 5212 |
. . . . 5
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13 | 9, 12 | ax-mp 5 |
. . . 4
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14 | dfdm4 5141 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 13, 14 | eqtr4i 2486 |
. . 3
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16 | 11, 15 | uneq12i 3617 |
. 2
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17 | unidm 3608 |
. 2
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18 | 7, 16, 17 | 3eqtrri 2488 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4522 ax-nul 4530 ax-pr 4640 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-rab 2808 df-v 3080 df-dif 3440 df-un 3442 df-in 3444 df-ss 3451 df-nul 3747 df-if 3901 df-pw 3971 df-sn 3987 df-pr 3989 df-op 3993 df-uni 4201 df-br 4402 df-opab 4460 df-xp 4955 df-rel 4956 df-cnv 4957 df-co 4958 df-dm 4959 df-rn 4960 df-res 4961 |
This theorem is referenced by: (None) |
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