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Mirrors > Home > ILE Home > Th. List > iotanul | Unicode version |
Description: Theorem 8.22 in [Quine] p. 57. This theorem is the result if there
isn't exactly one ![]() ![]() |
Ref | Expression |
---|---|
iotanul |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2029 |
. . 3
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2 | dfiota2 5179 |
. . . 4
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3 | alnex 1499 |
. . . . . . 7
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4 | ax-in2 615 |
. . . . . . . . . 10
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5 | 4 | alimi 1455 |
. . . . . . . . 9
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6 | ss2ab 3223 |
. . . . . . . . 9
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7 | 5, 6 | sylibr 134 |
. . . . . . . 8
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8 | dfnul2 3424 |
. . . . . . . 8
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9 | 7, 8 | sseqtrrdi 3204 |
. . . . . . 7
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10 | 3, 9 | sylbir 135 |
. . . . . 6
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11 | 10 | unissd 3833 |
. . . . 5
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12 | uni0 3836 |
. . . . 5
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13 | 11, 12 | sseqtrdi 3203 |
. . . 4
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14 | 2, 13 | eqsstrid 3201 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 1, 14 | sylnbi 678 |
. 2
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16 | ss0 3463 |
. 2
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17 | 15, 16 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-in 3135 df-ss 3142 df-nul 3423 df-sn 3598 df-uni 3810 df-iota 5178 |
This theorem is referenced by: tz6.12-2 5506 0fv 5550 riotaund 5864 0g0 12749 |
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