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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > zlmodzxzldeplem | Structured version Visualization version Unicode version |
Description: A and B are not equal. (Contributed by AV, 24-May-2019.) (Revised by AV, 10-Jun-2019.) |
Ref | Expression |
---|---|
zlmodzxzldep.z |
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zlmodzxzldep.a |
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zlmodzxzldep.b |
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Ref | Expression |
---|---|
zlmodzxzldeplem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 4681 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | opex 4681 |
. . . . 5
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3 | 1, 2 | pm3.2i 461 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | opex 4681 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | opex 4681 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 4, 5 | pm3.2i 461 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 3, 6 | pm3.2i 461 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 2re 10712 |
. . . . . . . 8
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9 | 2lt3 10811 |
. . . . . . . 8
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10 | 8, 9 | gtneii 9777 |
. . . . . . 7
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11 | 10 | olci 397 |
. . . . . 6
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12 | c0ex 9668 |
. . . . . . 7
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13 | 3ex 10718 |
. . . . . . 7
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14 | 12, 13 | opthne 4699 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 11, 14 | mpbir 214 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 0ne1 10710 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
17 | 16 | orci 396 |
. . . . . 6
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18 | 12, 13 | opthne 4699 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 17, 18 | mpbir 214 |
. . . . 5
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20 | 15, 19 | pm3.2i 461 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 20 | orci 396 |
. . 3
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22 | prneimg 4170 |
. . 3
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23 | 7, 21, 22 | mp2 9 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | zlmodzxzldep.a |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | zlmodzxzldep.b |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
26 | 24, 25 | neeq12i 2702 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 23, 26 | mpbir 214 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-un 6615 ax-resscn 9627 ax-1cn 9628 ax-icn 9629 ax-addcl 9630 ax-addrcl 9631 ax-mulcl 9632 ax-mulrcl 9633 ax-mulcom 9634 ax-addass 9635 ax-mulass 9636 ax-distr 9637 ax-i2m1 9638 ax-1ne0 9639 ax-1rid 9640 ax-rnegex 9641 ax-rrecex 9642 ax-cnre 9643 ax-pre-lttri 9644 ax-pre-lttrn 9645 ax-pre-ltadd 9646 ax-pre-mulgt0 9647 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-nel 2636 df-ral 2754 df-rex 2755 df-reu 2756 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-br 4419 df-opab 4478 df-mpt 4479 df-id 4771 df-po 4777 df-so 4778 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-riota 6282 df-ov 6323 df-oprab 6324 df-mpt2 6325 df-er 7394 df-en 7601 df-dom 7602 df-sdom 7603 df-pnf 9708 df-mnf 9709 df-xr 9710 df-ltxr 9711 df-le 9712 df-sub 9893 df-neg 9894 df-2 10701 df-3 10702 |
This theorem is referenced by: zlmodzxzldeplem1 40662 zlmodzxzldeplem3 40664 zlmodzxzldeplem4 40665 ldepsnlinc 40670 |
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