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Mirrors > Home > MPE Home > Th. List > bm1.1 | Structured version Visualization version Unicode version |
Description: Any set defined by a property is the only set defined by that property. Theorem 1.1 of [BellMachover] p. 462. (Contributed by NM, 30-Jun-1994.) (Proof shortened by Wolf Lammen, 13-Nov-2019.) |
Ref | Expression |
---|---|
bm1.1.1 |
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Ref | Expression |
---|---|
bm1.1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biantr 945 |
. . . . 5
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2 | 1 | alanimi 1696 |
. . . 4
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3 | ax-ext 2451 |
. . . 4
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4 | 2, 3 | syl 17 |
. . 3
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5 | 4 | gen2 1678 |
. 2
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6 | nfv 1769 |
. . . . . 6
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7 | bm1.1.1 |
. . . . . 6
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8 | 6, 7 | nfbi 2037 |
. . . . 5
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9 | 8 | nfal 2049 |
. . . 4
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10 | elequ2 1918 |
. . . . . 6
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11 | 10 | bibi1d 326 |
. . . . 5
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12 | 11 | albidv 1775 |
. . . 4
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13 | 9, 12 | mo4f 2365 |
. . 3
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14 | df-mo 2324 |
. . 3
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15 | 13, 14 | bitr3i 259 |
. 2
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16 | 5, 15 | mpbi 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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 |
This theorem is referenced by: zfnuleu 4523 |
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