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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > disjex | Structured version Visualization version Unicode version |
Description: Two ways to say that two classes are disjoint (or equal). (Contributed by Thierry Arnoux, 4-Oct-2016.) |
Ref | Expression |
---|---|
disjex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 393 |
. 2
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2 | df-in 3379 |
. . . . . 6
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3 | 2 | neeq1i 2688 |
. . . . 5
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4 | abn0 3719 |
. . . . 5
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5 | 3, 4 | bitr2i 258 |
. . . 4
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6 | 5 | necon2bbii 2675 |
. . 3
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7 | 6 | orbi2i 526 |
. 2
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8 | imor 418 |
. 2
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9 | 1, 7, 8 | 3bitr4ri 286 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-v 3015 df-dif 3375 df-in 3379 df-nul 3700 |
This theorem is referenced by: (None) |
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