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Mirrors > Home > MPE Home > Th. List > 0disj | Structured version Visualization version Unicode version |
Description: Any collection of empty sets is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
0disj | Disj |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ss 3972 | . . 3 | |
2 | 1 | rgenw 2924 | . 2 |
3 | sndisj 4644 | . 2 Disj | |
4 | disjss2 4623 | . 2 Disj Disj | |
5 | 2, 3, 4 | mp2 9 | 1 Disj |
Colors of variables: wff setvar class |
Syntax hints: wral 2912 wss 3574 c0 3915 csn 4177 Disj wdisj 4620 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rmo 2920 df-v 3202 df-dif 3577 df-in 3581 df-ss 3588 df-nul 3916 df-sn 4178 df-disj 4621 |
This theorem is referenced by: (None) |
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