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Mirrors > Home > MPE Home > Th. List > rpnnen1lem2 | Structured version Visualization version Unicode version |
Description: Lemma for rpnnen1 11285. (Contributed by Mario Carneiro, 12-May-2013.) |
Ref | Expression |
---|---|
rpnnen1.1 |
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rpnnen1.2 |
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Ref | Expression |
---|---|
rpnnen1lem2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpnnen1.1 |
. . 3
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2 | ssrab2 3482 |
. . 3
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3 | 1, 2 | eqsstri 3430 |
. 2
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4 | 3 | a1i 11 |
. . 3
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5 | nnre 10605 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | remulcl 9611 |
. . . . . . . . 9
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7 | 6 | ancoms 459 |
. . . . . . . 8
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8 | 5, 7 | sylan2 481 |
. . . . . . 7
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9 | btwnz 11027 |
. . . . . . . 8
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10 | 9 | simpld 465 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 8, 10 | syl 17 |
. . . . . 6
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12 | zre 10931 |
. . . . . . . . 9
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13 | 12 | adantl 472 |
. . . . . . . 8
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14 | simpll 765 |
. . . . . . . 8
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15 | nngt0 10627 |
. . . . . . . . . 10
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16 | 5, 15 | jca 539 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 16 | ad2antlr 738 |
. . . . . . . 8
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18 | ltdivmul 10469 |
. . . . . . . 8
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19 | 13, 14, 17, 18 | syl3anc 1271 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 19 | rexbidva 2870 |
. . . . . 6
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21 | 11, 20 | mpbird 240 |
. . . . 5
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22 | rabn0 3720 |
. . . . 5
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23 | 21, 22 | sylibr 217 |
. . . 4
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24 | 1 | neeq1i 2688 |
. . . 4
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25 | 23, 24 | sylibr 217 |
. . 3
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26 | 1 | rabeq2i 3010 |
. . . . . 6
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27 | 5 | ad2antlr 738 |
. . . . . . . . . 10
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28 | 27, 14, 6 | syl2anc 671 |
. . . . . . . . 9
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29 | ltle 9709 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
30 | 13, 28, 29 | syl2anc 671 |
. . . . . . . 8
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31 | 19, 30 | sylbid 223 |
. . . . . . 7
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32 | 31 | impr 629 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 26, 32 | sylan2b 482 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 33 | ralrimiva 2790 |
. . . 4
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35 | breq2 4378 |
. . . . . 6
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36 | 35 | ralbidv 2810 |
. . . . 5
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37 | 36 | rspcev 3118 |
. . . 4
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38 | 8, 34, 37 | syl2anc 671 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
39 | suprzcl 11005 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
40 | 4, 25, 38, 39 | syl3anc 1271 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
41 | 3, 40 | sseldi 3398 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-8 1893 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pow 4554 ax-pr 4612 ax-un 6571 ax-resscn 9583 ax-1cn 9584 ax-icn 9585 ax-addcl 9586 ax-addrcl 9587 ax-mulcl 9588 ax-mulrcl 9589 ax-mulcom 9590 ax-addass 9591 ax-mulass 9592 ax-distr 9593 ax-i2m1 9594 ax-1ne0 9595 ax-1rid 9596 ax-rnegex 9597 ax-rrecex 9598 ax-cnre 9599 ax-pre-lttri 9600 ax-pre-lttrn 9601 ax-pre-ltadd 9602 ax-pre-mulgt0 9603 ax-pre-sup 9604 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 987 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-nel 2625 df-ral 2742 df-rex 2743 df-reu 2744 df-rmo 2745 df-rab 2746 df-v 3015 df-sbc 3236 df-csb 3332 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-pss 3388 df-nul 3700 df-if 3850 df-pw 3921 df-sn 3937 df-pr 3939 df-tp 3941 df-op 3943 df-uni 4169 df-iun 4250 df-br 4375 df-opab 4434 df-mpt 4435 df-tr 4470 df-eprel 4723 df-id 4727 df-po 4733 df-so 4734 df-fr 4771 df-we 4773 df-xp 4818 df-rel 4819 df-cnv 4820 df-co 4821 df-dm 4822 df-rn 4823 df-res 4824 df-ima 4825 df-pred 5359 df-ord 5405 df-on 5406 df-lim 5407 df-suc 5408 df-iota 5525 df-fun 5563 df-fn 5564 df-f 5565 df-f1 5566 df-fo 5567 df-f1o 5568 df-fv 5569 df-riota 6238 df-ov 6279 df-oprab 6280 df-mpt2 6281 df-om 6681 df-wrecs 7015 df-recs 7077 df-rdg 7115 df-er 7350 df-en 7557 df-dom 7558 df-sdom 7559 df-sup 7943 df-pnf 9664 df-mnf 9665 df-xr 9666 df-ltxr 9667 df-le 9668 df-sub 9849 df-neg 9850 df-div 10259 df-nn 10599 df-n0 10860 df-z 10928 |
This theorem is referenced by: rpnnen1lem3 11282 rpnnen1lem5 11284 |
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