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Mirrors > Home > MPE Home > Th. List > dfoprab2 | Structured version Visualization version Unicode version |
Description: Class abstraction for operations in terms of class abstraction of ordered pairs. (Contributed by NM, 12-Mar-1995.) |
Ref | Expression |
---|---|
dfoprab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1938 |
. . . 4
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2 | exrot4 1943 |
. . . . 5
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3 | opeq1 4180 |
. . . . . . . . . . . 12
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4 | 3 | eqeq2d 2472 |
. . . . . . . . . . 11
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5 | 4 | pm5.32ri 648 |
. . . . . . . . . 10
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6 | 5 | anbi1i 706 |
. . . . . . . . 9
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7 | anass 659 |
. . . . . . . . 9
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8 | an32 812 |
. . . . . . . . 9
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9 | 6, 7, 8 | 3bitr3i 283 |
. . . . . . . 8
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10 | 9 | exbii 1729 |
. . . . . . 7
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11 | opex 4681 |
. . . . . . . . 9
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12 | 11 | isseti 3063 |
. . . . . . . 8
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13 | 19.42v 1845 |
. . . . . . . 8
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14 | 12, 13 | mpbiran2 935 |
. . . . . . 7
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15 | 10, 14 | bitri 257 |
. . . . . 6
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16 | 15 | 3exbii 1731 |
. . . . 5
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17 | 2, 16 | bitri 257 |
. . . 4
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18 | 19.42vv 1847 |
. . . . 5
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19 | 18 | 2exbii 1730 |
. . . 4
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20 | 1, 17, 19 | 3bitr3i 283 |
. . 3
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21 | 20 | abbii 2578 |
. 2
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22 | df-oprab 6324 |
. 2
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23 | df-opab 4478 |
. 2
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24 | 21, 22, 23 | 3eqtr4i 2494 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4541 ax-nul 4550 ax-pr 4656 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-opab 4478 df-oprab 6324 |
This theorem is referenced by: reloprab 6370 oprabv 6371 cbvoprab1 6395 cbvoprab12 6397 cbvoprab3 6399 dmoprab 6409 rnoprab 6411 ssoprab2i 6417 mpt2mptx 6419 resoprab 6424 funoprabg 6427 elrnmpt2res 6442 ov6g 6466 dfoprab3s 6880 xpcomco 7693 omxpenlem 7704 nvss 26268 mpt2mptxf 28332 bj-dfmpt2a 31676 mpt2mptx2 40485 |
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