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Mathbox for Scott Fenton |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfint3 | Structured version Visualization version Unicode version |
Description: Quantifier-free definition of class intersection. (Contributed by Scott Fenton, 13-Apr-2018.) |
Ref | Expression |
---|---|
dfint3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfint2 4250 |
. 2
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2 | ralnex 2846 |
. . . 4
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3 | vex 3060 |
. . . . . . . . 9
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4 | vex 3060 |
. . . . . . . . 9
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5 | 3, 4 | brcnv 5039 |
. . . . . . . 8
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6 | brv 30694 |
. . . . . . . . 9
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7 | brdif 4469 |
. . . . . . . . 9
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8 | 6, 7 | mpbiran 934 |
. . . . . . . 8
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9 | 5, 8 | bitr2i 258 |
. . . . . . 7
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10 | 9 | con1bii 337 |
. . . . . 6
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11 | epel 4770 |
. . . . . 6
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12 | 10, 11 | bitr2i 258 |
. . . . 5
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13 | 12 | ralbii 2831 |
. . . 4
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14 | eldif 3426 |
. . . . . 6
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15 | 4, 14 | mpbiran 934 |
. . . . 5
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16 | 4 | elima 5195 |
. . . . 5
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17 | 15, 16 | xchbinx 316 |
. . . 4
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18 | 2, 13, 17 | 3bitr4ri 286 |
. . 3
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19 | 18 | abbi2i 2577 |
. 2
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20 | 1, 19 | eqtr4i 2487 |
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-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 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-int 4249 df-br 4419 df-opab 4478 df-eprel 4767 df-xp 4862 df-cnv 4864 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 |
This theorem is referenced by: (None) |
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