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Mirrors > Home > NFE Home > Th. List > uneqdifeq | Unicode version |
Description: Two ways to say that ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
uneqdifeq |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uncom 3409 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | eqtr 2370 |
. . . . . . 7
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3 | 2 | eqcomd 2358 |
. . . . . 6
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4 | difeq1 3247 |
. . . . . . 7
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5 | difun2 3630 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | eqtr 2370 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | incom 3449 |
. . . . . . . . . . 11
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8 | 7 | eqeq1i 2360 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | disj3 3596 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 8, 9 | bitri 240 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | eqtr 2370 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 11 | expcom 424 |
. . . . . . . . . 10
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13 | 12 | eqcoms 2356 |
. . . . . . . . 9
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14 | 10, 13 | sylbi 187 |
. . . . . . . 8
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15 | 6, 14 | syl5com 26 |
. . . . . . 7
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16 | 4, 5, 15 | sylancl 643 |
. . . . . 6
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17 | 3, 16 | syl 15 |
. . . . 5
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18 | 1, 17 | mpan 651 |
. . . 4
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19 | 18 | com12 27 |
. . 3
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20 | 19 | adantl 452 |
. 2
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21 | difss 3394 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | sseq1 3293 |
. . . . . . . . 9
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23 | unss 3438 |
. . . . . . . . . . 11
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24 | 23 | biimpi 186 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 24 | expcom 424 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 22, 25 | syl6bi 219 |
. . . . . . . 8
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27 | 21, 26 | mpi 16 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 27 | com12 27 |
. . . . . 6
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29 | 28 | adantr 451 |
. . . . 5
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30 | 29 | imp 418 |
. . . 4
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31 | eqimss 3324 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
32 | 31 | adantl 452 |
. . . . . 6
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33 | ssundif 3634 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
34 | 32, 33 | sylibr 203 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 34 | adantlr 695 |
. . . 4
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36 | 30, 35 | eqssd 3290 |
. . 3
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37 | 36 | ex 423 |
. 2
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38 | 20, 37 | impbid 183 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ne 2519 df-ral 2620 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-ss 3260 df-nul 3552 |
This theorem is referenced by: (None) |
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