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Mirrors > Home > MPE Home > Th. List > snex | Structured version Visualization version Unicode version |
Description: A singleton is a set. Theorem 7.12 of [Quine] p. 51, proved using Extensionality, Separation, Null Set, and Pairing. See also snexALT 4606. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 19-May-2013.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
snex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 3993 |
. . 3
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2 | preq12 4066 |
. . . . . 6
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3 | 2 | anidms 655 |
. . . . 5
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4 | 3 | eleq1d 2524 |
. . . 4
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5 | zfpair2 4657 |
. . . 4
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6 | 4, 5 | vtoclg 3119 |
. . 3
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7 | 1, 6 | syl5eqel 2544 |
. 2
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8 | snprc 4048 |
. . . 4
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9 | 8 | biimpi 199 |
. . 3
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10 | 0ex 4551 |
. . 3
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11 | 9, 10 | syl6eqel 2548 |
. 2
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12 | 7, 11 | pm2.61i 169 |
1
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