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Mirrors > Home > NFE Home > Th. List > 0nel1c | Unicode version |
Description: The empty class is not a singleton. (Contributed by SF, 22-Jan-2015.) |
Ref | Expression |
---|---|
0nel1c |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2863 |
. . . 4
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2 | snprc 3789 |
. . . . . 6
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3 | eqcom 2355 |
. . . . . 6
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4 | 2, 3 | bitri 240 |
. . . . 5
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5 | 4 | con1bii 321 |
. . . 4
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6 | 1, 5 | mpbir 200 |
. . 3
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7 | 6 | nex 1555 |
. 2
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8 | el1c 4140 |
. 2
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9 | 7, 8 | mtbir 290 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4079 ax-sn 4088 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ne 2519 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-ss 3260 df-nul 3552 df-sn 3742 df-1c 4137 |
This theorem is referenced by: pw10 4162 vfin1cltv 4548 |
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