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Mirrors > Home > MPE Home > Th. List > brdif | Structured version Visualization version Unicode version |
Description: The difference of two binary relations. (Contributed by Scott Fenton, 11-Apr-2011.) |
Ref | Expression |
---|---|
brdif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3413 |
. 2
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2 | df-br 4402 |
. 2
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3 | df-br 4402 |
. . 3
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4 | df-br 4402 |
. . . 4
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5 | 4 | notbii 298 |
. . 3
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6 | 3, 5 | anbi12i 702 |
. 2
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7 | 1, 2, 6 | 3bitr4i 281 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-v 3046 df-dif 3406 df-br 4402 |
This theorem is referenced by: fndmdif 5984 isocnv3 6221 brdifun 7387 dflt2 11444 pltval 16199 ltgov 24635 opeldifid 28203 qtophaus 28656 dftr6 30383 dffr5 30386 fundmpss 30400 brsset 30649 dfon3 30652 brtxpsd2 30655 dffun10 30674 elfuns 30675 dfrecs2 30710 dfrdg4 30711 dfint3 30712 brub 30714 broutsideof 30881 frege124d 36347 |
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