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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-0nelsngl | Structured version Visualization version Unicode version |
Description: The empty set is not a member of a singletonization (neither is any nonsingleton, in particular any von Neuman ordinal except possibly df-1o 7182). (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
bj-0nelsngl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3048 |
. . . . . 6
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2 | 1 | snnz 4090 |
. . . . 5
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3 | 2 | nesymi 2681 |
. . . 4
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4 | 3 | nex 1678 |
. . 3
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5 | bj-elsngl 31562 |
. . . 4
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6 | rexex 2844 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | sylbi 199 |
. . 3
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8 | 4, 7 | mto 180 |
. 2
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9 | 8 | nelir 2727 |
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 |
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-nel 2625 df-ral 2742 df-rex 2743 df-v 3047 df-dif 3407 df-un 3409 df-nul 3732 df-sn 3969 df-pr 3971 df-bj-sngl 31560 |
This theorem is referenced by: (None) |
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