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Mirrors > Home > ILE Home > Th. List > zfregfr | Unicode version |
Description: The epsilon relation is well-founded on any class. (Contributed by NM, 26-Nov-1995.) |
Ref | Expression |
---|---|
zfregfr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-frind 4262 |
. 2
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2 | bi2.04 247 |
. . . . . . 7
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3 | 2 | albii 1447 |
. . . . . 6
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4 | df-ral 2422 |
. . . . . 6
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5 | 3, 4 | bitr4i 186 |
. . . . 5
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6 | sbim 1927 |
. . . . . . . . . . 11
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7 | clelsb3 2245 |
. . . . . . . . . . . 12
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8 | clelsb3 2245 |
. . . . . . . . . . . 12
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9 | 7, 8 | imbi12i 238 |
. . . . . . . . . . 11
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10 | 6, 9 | bitri 183 |
. . . . . . . . . 10
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11 | 10 | ralbii 2444 |
. . . . . . . . 9
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12 | ralcom3 2601 |
. . . . . . . . 9
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13 | 11, 12 | bitri 183 |
. . . . . . . 8
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14 | epel 4222 |
. . . . . . . . . 10
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15 | 14 | imbi1i 237 |
. . . . . . . . 9
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16 | 15 | ralbii 2444 |
. . . . . . . 8
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17 | 13, 16 | bitr4i 186 |
. . . . . . 7
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18 | 17 | imbi1i 237 |
. . . . . 6
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19 | 18 | ralbii 2444 |
. . . . 5
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20 | 5, 19 | bitri 183 |
. . . 4
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21 | ax-setind 4460 |
. . . . 5
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22 | dfss2 3091 |
. . . . 5
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23 | 21, 22 | sylibr 133 |
. . . 4
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24 | 20, 23 | sylbir 134 |
. . 3
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25 | df-frfor 4261 |
. . 3
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26 | 24, 25 | mpbir 145 |
. 2
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27 | 1, 26 | mpgbir 1430 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-setind 4460 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-eprel 4219 df-frfor 4261 df-frind 4262 |
This theorem is referenced by: ordfr 4497 wessep 4500 reg3exmidlemwe 4501 |
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