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Mirrors > Home > MPE Home > Th. List > resoprab | Structured version Visualization version Unicode version |
Description: Restriction of an operation class abstraction. (Contributed by NM, 10-Feb-2007.) |
Ref | Expression |
---|---|
resoprab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resopab 5128 |
. . 3
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2 | 19.42vv 1839 |
. . . . 5
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3 | an12 811 |
. . . . . . 7
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4 | eleq1 2517 |
. . . . . . . . . 10
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5 | opelxp 4841 |
. . . . . . . . . 10
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6 | 4, 5 | syl6bb 269 |
. . . . . . . . 9
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7 | 6 | anbi1d 716 |
. . . . . . . 8
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8 | 7 | pm5.32i 647 |
. . . . . . 7
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9 | 3, 8 | bitri 257 |
. . . . . 6
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10 | 9 | 2exbii 1722 |
. . . . 5
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11 | 2, 10 | bitr3i 259 |
. . . 4
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12 | 11 | opabbii 4438 |
. . 3
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13 | 1, 12 | eqtri 2473 |
. 2
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14 | dfoprab2 6324 |
. . 3
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15 | 14 | reseq1i 5078 |
. 2
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16 | dfoprab2 6324 |
. 2
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17 | 13, 15, 16 | 3eqtr4i 2483 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-9 1899 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 ax-sep 4496 ax-nul 4505 ax-pr 4611 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3014 df-dif 3374 df-un 3376 df-in 3378 df-ss 3385 df-nul 3699 df-if 3849 df-sn 3936 df-pr 3938 df-op 3942 df-opab 4433 df-xp 4817 df-rel 4818 df-res 4823 df-oprab 6279 |
This theorem is referenced by: resoprab2 6380 df1stres 28291 df2ndres 28292 |
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