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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-disjcsn | Structured version Visualization version Unicode version |
Description: A class is disjoint from its singleton. A consequence of regularity. Shorter proof than bnj521 29545. (Contributed by BJ, 4-Apr-2019.) |
Ref | Expression |
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bj-disjcsn |
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Step | Hyp | Ref | Expression |
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1 | elirr 8113 |
. 2
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2 | disjsn 4032 |
. 2
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3 | 1, 2 | mpbir 213 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 ax-reg 8107 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-nul 3732 df-sn 3969 df-pr 3971 |
This theorem is referenced by: (None) |
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