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Mirrors > Home > ILE Home > Th. List > iotaval | Unicode version |
Description: Theorem 8.19 in [Quine] p. 57. This theorem is the fundamental property of iota. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotaval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfiota2 4918 |
. 2
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2 | vex 2613 |
. . . . . . 7
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3 | sbeqalb 2879 |
. . . . . . . 8
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4 | equcomi 1633 |
. . . . . . . 8
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5 | 3, 4 | syl6 33 |
. . . . . . 7
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6 | 2, 5 | ax-mp 7 |
. . . . . 6
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7 | 6 | ex 113 |
. . . . 5
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8 | equequ2 1641 |
. . . . . . . . . 10
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9 | 8 | equcoms 1636 |
. . . . . . . . 9
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10 | 9 | bibi2d 230 |
. . . . . . . 8
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11 | 10 | biimpd 142 |
. . . . . . 7
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12 | 11 | alimdv 1802 |
. . . . . 6
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13 | 12 | com12 30 |
. . . . 5
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14 | 7, 13 | impbid 127 |
. . . 4
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15 | 14 | alrimiv 1797 |
. . 3
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16 | uniabio 4927 |
. . 3
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17 | 15, 16 | syl 14 |
. 2
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18 | 1, 17 | syl5eq 2127 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-rex 2359 df-v 2612 df-sbc 2825 df-un 2986 df-sn 3422 df-pr 3423 df-uni 3622 df-iota 4917 |
This theorem is referenced by: iotauni 4929 iota1 4931 euiotaex 4933 iota4 4935 iota5 4937 |
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