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Mirrors > Home > MPE Home > Th. List > inundif | Structured version Visualization version Unicode version |
Description: The intersection and class difference of a class with another class unite to give the original class. (Contributed by Paul Chapman, 5-Jun-2009.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
inundif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3628 |
. . . 4
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2 | eldif 3425 |
. . . 4
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3 | 1, 2 | orbi12i 528 |
. . 3
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4 | pm4.42 977 |
. . 3
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5 | 3, 4 | bitr4i 260 |
. 2
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6 | 5 | uneqri 3587 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-v 3058 df-dif 3418 df-un 3420 df-in 3422 |
This theorem is referenced by: resasplit 5775 fresaun 5776 fresaunres2 5777 ixpfi2 7897 hashun3 12594 prmreclem2 14909 mvdco 17134 sylow2a 17319 ablfac1eu 17754 basdif0 20016 neitr 20244 cmpfi 20471 ptbasfi 20644 ptcnplem 20684 fin1aufil 20995 ismbl2 22529 volinun 22547 voliunlem2 22552 mbfeqalem 22646 itg2cnlem2 22768 dvres2lem 22913 indifundif 28200 iunxdif3 28223 imadifxp 28260 ofpreima2 28317 partfun 28326 resf1o 28363 gsummptres 28595 measun 29081 measunl 29086 inelcarsg 29191 carsgclctun 29201 sibfof 29221 probdif 29301 mthmpps 30268 clcnvlem 36274 radcnvrat 36706 sumnnodd 37747 omelesplit 38376 |
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