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Mirrors > Home > MPE Home > Th. List > frsn | Structured version Visualization version Unicode version |
Description: Founded relation on a singleton. (Contributed by Mario Carneiro, 28-Dec-2014.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
frsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fr 4770 |
. . . 4
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2 | df-ne 2623 |
. . . . . . . . . 10
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3 | simpr 467 |
. . . . . . . . . . . 12
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4 | sssn 4098 |
. . . . . . . . . . . 12
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5 | 3, 4 | sylib 201 |
. . . . . . . . . . 11
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6 | 5 | ord 383 |
. . . . . . . . . 10
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7 | 2, 6 | syl5bi 225 |
. . . . . . . . 9
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8 | 7 | impr 629 |
. . . . . . . 8
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9 | eqimss 3451 |
. . . . . . . . . 10
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10 | 9 | adantl 472 |
. . . . . . . . 9
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11 | simpr 467 |
. . . . . . . . . 10
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12 | snnzg 4057 |
. . . . . . . . . . 11
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13 | 12 | ad2antlr 738 |
. . . . . . . . . 10
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14 | 11, 13 | eqnetrd 2690 |
. . . . . . . . 9
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15 | 10, 14 | jca 539 |
. . . . . . . 8
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16 | 8, 15 | impbida 847 |
. . . . . . 7
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17 | 16 | imbi1d 323 |
. . . . . 6
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18 | 17 | albidv 1770 |
. . . . 5
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19 | snex 4613 |
. . . . . 6
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20 | raleq 2954 |
. . . . . . 7
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21 | 20 | rexeqbi1dv 2963 |
. . . . . 6
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22 | 19, 21 | ceqsalv 3042 |
. . . . 5
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23 | 18, 22 | syl6bb 269 |
. . . 4
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24 | 1, 23 | syl5bb 265 |
. . 3
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25 | breq2 4377 |
. . . . . . . 8
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26 | 25 | notbid 300 |
. . . . . . 7
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27 | 26 | ralbidv 2809 |
. . . . . 6
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28 | 27 | rexsng 3974 |
. . . . 5
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29 | breq1 4376 |
. . . . . . 7
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30 | 29 | notbid 300 |
. . . . . 6
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31 | 30 | ralsng 3973 |
. . . . 5
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32 | 28, 31 | bitrd 261 |
. . . 4
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33 | 32 | adantl 472 |
. . 3
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34 | 24, 33 | bitrd 261 |
. 2
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35 | snprc 4003 |
. . . . 5
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36 | fr0 4790 |
. . . . . 6
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37 | freq2 4782 |
. . . . . 6
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38 | 36, 37 | mpbiri 241 |
. . . . 5
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39 | 35, 38 | sylbi 200 |
. . . 4
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40 | 39 | adantl 472 |
. . 3
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41 | brrelex 4850 |
. . . 4
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42 | 41 | stoic1a 1658 |
. . 3
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43 | 40, 42 | 2thd 248 |
. 2
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44 | 34, 43 | pm2.61dan 805 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-9 1899 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 ax-sep 4496 ax-nul 4505 ax-pr 4611 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3014 df-sbc 3235 df-dif 3374 df-un 3376 df-in 3378 df-ss 3385 df-nul 3699 df-if 3849 df-sn 3936 df-pr 3938 df-op 3942 df-br 4374 df-opab 4433 df-fr 4770 df-xp 4817 df-rel 4818 |
This theorem is referenced by: wesn 4883 |
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