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Mathbox for Jeff Madsen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rngoisoval | Structured version Visualization version Unicode version |
Description: The set of ring isomorphisms. (Contributed by Jeff Madsen, 16-Jun-2011.) |
Ref | Expression |
---|---|
rngisoval.1 |
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rngisoval.2 |
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rngisoval.3 |
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rngisoval.4 |
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Ref | Expression |
---|---|
rngoisoval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq12 6323 |
. . 3
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2 | fveq2 5887 |
. . . . . . . 8
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3 | rngisoval.1 |
. . . . . . . 8
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4 | 2, 3 | syl6eqr 2513 |
. . . . . . 7
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5 | 4 | rneqd 5080 |
. . . . . 6
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6 | rngisoval.2 |
. . . . . 6
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7 | 5, 6 | syl6eqr 2513 |
. . . . 5
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8 | f1oeq2 5828 |
. . . . 5
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9 | 7, 8 | syl 17 |
. . . 4
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10 | fveq2 5887 |
. . . . . . . 8
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11 | rngisoval.3 |
. . . . . . . 8
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12 | 10, 11 | syl6eqr 2513 |
. . . . . . 7
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13 | 12 | rneqd 5080 |
. . . . . 6
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14 | rngisoval.4 |
. . . . . 6
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15 | 13, 14 | syl6eqr 2513 |
. . . . 5
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16 | f1oeq3 5829 |
. . . . 5
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17 | 15, 16 | syl 17 |
. . . 4
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18 | 9, 17 | sylan9bb 711 |
. . 3
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19 | 1, 18 | rabeqbidv 3051 |
. 2
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20 | df-rngoiso 32259 |
. 2
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21 | ovex 6342 |
. . 3
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22 | 21 | rabex 4567 |
. 2
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23 | 19, 20, 22 | ovmpt2a 6453 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pr 4652 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-rab 2757 df-v 3058 df-sbc 3279 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-uni 4212 df-br 4416 df-opab 4475 df-id 4767 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-iota 5564 df-fun 5602 df-fn 5603 df-f 5604 df-f1 5605 df-fo 5606 df-f1o 5607 df-fv 5608 df-ov 6317 df-oprab 6318 df-mpt2 6319 df-rngoiso 32259 |
This theorem is referenced by: isrngoiso 32261 |
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