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Mirrors > Home > MPE Home > Th. List > uneqdifeq | Structured version Visualization version Unicode version |
Description: Two ways to say that ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
uneqdifeq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uncom 3590 |
. . . . 5
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2 | eqtr 2481 |
. . . . . . 7
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3 | 2 | eqcomd 2468 |
. . . . . 6
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4 | difeq1 3556 |
. . . . . . 7
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5 | difun2 3859 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | eqtr 2481 |
. . . . . . . 8
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7 | incom 3637 |
. . . . . . . . . . 11
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8 | 7 | eqeq1i 2467 |
. . . . . . . . . 10
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9 | disj3 3821 |
. . . . . . . . . 10
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10 | 8, 9 | bitri 257 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | eqtr 2481 |
. . . . . . . . . . 11
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12 | 11 | expcom 441 |
. . . . . . . . . 10
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13 | 12 | eqcoms 2470 |
. . . . . . . . 9
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14 | 10, 13 | sylbi 200 |
. . . . . . . 8
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15 | 6, 14 | syl5com 31 |
. . . . . . 7
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16 | 4, 5, 15 | sylancl 673 |
. . . . . 6
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17 | 3, 16 | syl 17 |
. . . . 5
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18 | 1, 17 | mpan 681 |
. . . 4
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19 | 18 | com12 32 |
. . 3
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20 | 19 | adantl 472 |
. 2
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21 | difss 3572 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | sseq1 3465 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | unss 3620 |
. . . . . . . . . . 11
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24 | 23 | biimpi 199 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 24 | expcom 441 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 22, 25 | syl6bi 236 |
. . . . . . . 8
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27 | 21, 26 | mpi 20 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 27 | com12 32 |
. . . . . 6
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29 | 28 | adantr 471 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 29 | imp 435 |
. . . 4
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31 | eqimss 3496 |
. . . . . . 7
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32 | 31 | adantl 472 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | ssundif 3863 |
. . . . . 6
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34 | 32, 33 | sylibr 217 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 34 | adantlr 726 |
. . . 4
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36 | 30, 35 | eqssd 3461 |
. . 3
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37 | 36 | ex 440 |
. 2
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38 | 20, 37 | impbid 195 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 |
This theorem is referenced by: fzdifsuc 11884 hashbclem 12648 lecldbas 20284 conndisj 20480 ptuncnv 20871 ptunhmeo 20872 cldsubg 21174 icopnfcld 21837 iocmnfcld 21838 voliunlem1 22552 icombl 22566 ioombl 22567 uniioombllem4 22593 ismbf3d 22659 lhop 23017 subfacp1lem3 29954 subfacp1lem5 29956 pconcon 30003 cvmscld 30045 |
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