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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > iundifdifd | Structured version Visualization version Unicode version |
Description: The intersection of a set is the complement of the union of the complements. (Contributed by Thierry Arnoux, 19-Dec-2016.) |
Ref | Expression |
---|---|
iundifdifd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iundif2 4359 |
. . . . 5
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2 | intiin 4346 |
. . . . . 6
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3 | 2 | difeq2i 3560 |
. . . . 5
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4 | 1, 3 | eqtr4i 2487 |
. . . 4
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5 | 4 | difeq2i 3560 |
. . 3
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6 | intssuni2 4274 |
. . . . 5
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7 | unipw 4664 |
. . . . 5
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8 | 6, 7 | syl6sseq 3490 |
. . . 4
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9 | dfss4 3689 |
. . . 4
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10 | 8, 9 | sylib 201 |
. . 3
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11 | 5, 10 | syl5req 2509 |
. 2
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12 | 11 | ex 440 |
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 4539 ax-nul 4548 ax-pr 4653 |
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-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-pw 3965 df-sn 3981 df-pr 3983 df-uni 4213 df-int 4249 df-iun 4294 df-iin 4295 |
This theorem is referenced by: sigaclci 29003 |
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