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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 5047 |
. 2
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2 | vex 2660 |
. . . . . . 7
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3 | sbeqalb 2933 |
. . . . . . . 8
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4 | equcomi 1663 |
. . . . . . . 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 114 |
. . . . 5
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8 | equequ2 1672 |
. . . . . . . . . 10
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9 | 8 | equcoms 1667 |
. . . . . . . . 9
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10 | 9 | bibi2d 231 |
. . . . . . . 8
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11 | 10 | biimpd 143 |
. . . . . . 7
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12 | 11 | alimdv 1833 |
. . . . . 6
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13 | 12 | com12 30 |
. . . . 5
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14 | 7, 13 | impbid 128 |
. . . 4
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15 | 14 | alrimiv 1828 |
. . 3
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16 | uniabio 5056 |
. . 3
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17 | 15, 16 | syl 14 |
. 2
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18 | 1, 17 | syl5eq 2159 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rex 2396 df-v 2659 df-sbc 2879 df-un 3041 df-sn 3499 df-pr 3500 df-uni 3703 df-iota 5046 |
This theorem is referenced by: iotauni 5058 iota1 5060 euiotaex 5062 iota4 5064 iota5 5066 |
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