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Mirrors > Home > HSE Home > Th. List > mddmd2 | Structured version Unicode version |
Description: Relationship between modular pairs and dual-modular pairs. Lemma 1.2 of [MaedaMaeda] p. 1. (Contributed by NM, 21-Jun-2004.) (New usage is discouraged.) |
Ref | Expression |
---|---|
mddmd2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 4391 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | cbvralv 3040 |
. . . 4
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3 | mdbr 25830 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | incom 3638 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | chjcom 25041 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 5 | ineq1d 3646 |
. . . . . . . . . . . 12
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7 | 4, 6 | syl5reqr 2506 |
. . . . . . . . . . 11
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8 | 7 | adantlr 714 |
. . . . . . . . . 10
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9 | incom 3638 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 9 | oveq1i 6197 |
. . . . . . . . . . 11
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11 | chincl 25034 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | chjcom 25041 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 11, 12 | sylan 471 |
. . . . . . . . . . 11
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14 | 10, 13 | syl5reqr 2506 |
. . . . . . . . . 10
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15 | 8, 14 | eqeq12d 2472 |
. . . . . . . . 9
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16 | eqcom 2459 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 15, 16 | syl6bb 261 |
. . . . . . . 8
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18 | 17 | imbi2d 316 |
. . . . . . 7
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19 | 18 | ralbidva 2833 |
. . . . . 6
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20 | 3, 19 | bitrd 253 |
. . . . 5
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21 | 20 | ralbidva 2833 |
. . . 4
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22 | 2, 21 | syl5bb 257 |
. . 3
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23 | ralcom 2974 |
. . 3
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24 | 22, 23 | syl6bb 261 |
. 2
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25 | dmdbr 25835 |
. . 3
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26 | 25 | ralbidva 2833 |
. 2
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27 | 24, 26 | bitr4d 256 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-rep 4498 ax-sep 4508 ax-nul 4516 ax-pow 4565 ax-pr 4626 ax-un 6469 ax-cnex 9436 ax-resscn 9437 ax-1cn 9438 ax-icn 9439 ax-addcl 9440 ax-addrcl 9441 ax-mulcl 9442 ax-mulrcl 9443 ax-i2m1 9448 ax-1ne0 9449 ax-rrecex 9452 ax-cnre 9453 ax-hilex 24533 ax-hfvadd 24534 ax-hv0cl 24537 ax-hfvmul 24539 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2599 df-ne 2644 df-ral 2798 df-rex 2799 df-reu 2800 df-rab 2802 df-v 3067 df-sbc 3282 df-csb 3384 df-dif 3426 df-un 3428 df-in 3430 df-ss 3437 df-pss 3439 df-nul 3733 df-if 3887 df-pw 3957 df-sn 3973 df-pr 3975 df-tp 3977 df-op 3979 df-uni 4187 df-int 4224 df-iun 4268 df-br 4388 df-opab 4446 df-mpt 4447 df-tr 4481 df-eprel 4727 df-id 4731 df-po 4736 df-so 4737 df-fr 4774 df-we 4776 df-ord 4817 df-on 4818 df-lim 4819 df-suc 4820 df-xp 4941 df-rel 4942 df-cnv 4943 df-co 4944 df-dm 4945 df-rn 4946 df-res 4947 df-ima 4948 df-iota 5476 df-fun 5515 df-fn 5516 df-f 5517 df-f1 5518 df-fo 5519 df-f1o 5520 df-fv 5521 df-ov 6190 df-oprab 6191 df-mpt2 6192 df-om 6574 df-recs 6929 df-rdg 6963 df-map 7313 df-nn 10421 df-hlim 24506 df-sh 24741 df-ch 24756 df-chj 24845 df-md 25816 df-dmd 25817 |
This theorem is referenced by: atmd 25935 |
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