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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 5197 |
. 2
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2 | vex 2755 |
. . . . . . 7
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3 | sbeqalb 3034 |
. . . . . . . 8
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4 | equcomi 1715 |
. . . . . . . 8
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5 | 3, 4 | syl6 33 |
. . . . . . 7
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6 | 2, 5 | ax-mp 5 |
. . . . . 6
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7 | 6 | ex 115 |
. . . . 5
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8 | equequ2 1724 |
. . . . . . . . . 10
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9 | 8 | equcoms 1719 |
. . . . . . . . 9
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10 | 9 | bibi2d 232 |
. . . . . . . 8
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11 | 10 | biimpd 144 |
. . . . . . 7
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12 | 11 | alimdv 1890 |
. . . . . 6
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13 | 12 | com12 30 |
. . . . 5
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14 | 7, 13 | impbid 129 |
. . . 4
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15 | 14 | alrimiv 1885 |
. . 3
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16 | uniabio 5206 |
. . 3
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17 | 15, 16 | syl 14 |
. 2
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18 | 1, 17 | eqtrid 2234 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-sn 3613 df-pr 3614 df-uni 3825 df-iota 5196 |
This theorem is referenced by: iotauni 5208 iota1 5210 euiotaex 5212 iota4 5215 iota5 5217 |
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