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Mathbox for Stefan O'Rear |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wopprc | Structured version Visualization version Unicode version |
Description: Unrelated: Wiener pairs treat proper classes symmetrically. (Contributed by Stefan O'Rear, 19-Sep-2014.) |
Ref | Expression |
---|---|
wopprc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 3981 |
. . . . . . . . 9
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2 | id 22 |
. . . . . . . . 9
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3 | 1, 2 | syl5reqr 2500 |
. . . . . . . 8
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4 | snex 4641 |
. . . . . . . . 9
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5 | 0ex 4535 |
. . . . . . . . 9
![]() ![]() ![]() ![]() | |
6 | 4, 5 | preqr1 4148 |
. . . . . . . 8
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7 | 3, 6 | syl 17 |
. . . . . . 7
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8 | snprc 4035 |
. . . . . . 7
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9 | 7, 8 | sylibr 216 |
. . . . . 6
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10 | 8 | biimpi 198 |
. . . . . . . 8
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11 | 10 | preq1d 4057 |
. . . . . . 7
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12 | 11, 1 | syl6reqr 2504 |
. . . . . 6
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13 | 9, 12 | impbii 191 |
. . . . 5
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14 | 13 | con2bii 334 |
. . . 4
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15 | snprc 4035 |
. . . . . . 7
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16 | eqcom 2458 |
. . . . . . 7
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17 | 15, 16 | bitr2i 254 |
. . . . . 6
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18 | 17 | con2bii 334 |
. . . . 5
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19 | 5 | sneqr 4139 |
. . . . . 6
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20 | sneq 3978 |
. . . . . 6
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21 | 19, 20 | impbii 191 |
. . . . 5
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22 | 18, 21 | xchbinxr 313 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 14, 22 | anbi12i 703 |
. . 3
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24 | pm4.56 498 |
. . . 4
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25 | snex 4641 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
26 | 25 | elpr 3986 |
. . . 4
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27 | 24, 26 | xchbinxr 313 |
. . 3
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28 | 23, 27 | bitri 253 |
. 2
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29 | df1o2 7194 |
. . 3
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30 | 29 | eleq1i 2520 |
. 2
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31 | 28, 30 | xchbinxr 313 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-v 3047 df-dif 3407 df-un 3409 df-nul 3732 df-sn 3969 df-pr 3971 df-suc 5429 df-1o 7182 |
This theorem is referenced by: (None) |
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