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Mirrors > Home > MPE Home > Th. List > disjx0 | Structured version Visualization version Unicode version |
Description: An empty collection is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
disjx0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ss 3730 |
. 2
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2 | disjxsn 4367 |
. 2
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3 | disjss1 4350 |
. 2
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4 | 1, 2, 3 | mp2 9 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-rmo 2744 df-v 3014 df-dif 3374 df-in 3378 df-ss 3385 df-nul 3699 df-sn 3936 df-disj 4345 |
This theorem is referenced by: (None) |
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