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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemb2 | Structured version Unicode version |
Description: Given two atoms not under
the fiducial (reference) co-atom ![]() |
Ref | Expression |
---|---|
cdlemb2.l |
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cdlemb2.j |
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cdlemb2.a |
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cdlemb2.h |
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Ref | Expression |
---|---|
cdlemb2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1l 1012 |
. 2
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2 | simp2ll 1055 |
. 2
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3 | simp2rl 1057 |
. 2
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4 | simp1r 1013 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | eqid 2451 |
. . . 4
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6 | cdlemb2.h |
. . . 4
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7 | 5, 6 | lhpbase 33945 |
. . 3
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8 | 4, 7 | syl 16 |
. 2
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9 | simp3 990 |
. 2
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10 | eqid 2451 |
. . . 4
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11 | eqid 2451 |
. . . 4
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12 | 10, 11, 6 | lhp1cvr 33946 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 12 | 3ad2ant1 1009 |
. 2
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14 | simp2lr 1056 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | simp2rr 1058 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | cdlemb2.l |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | cdlemb2.j |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | cdlemb2.a |
. . 3
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19 | 5, 16, 17, 10, 11, 18 | cdlemb 33741 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 1, 2, 3, 8, 9, 13, 14, 15, 19 | syl323anc 1249 |
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 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 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 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-nul 3733 df-if 3887 df-pw 3957 df-sn 3973 df-pr 3975 df-op 3979 df-uni 4187 df-iun 4268 df-br 4388 df-opab 4446 df-mpt 4447 df-id 4731 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-riota 6148 df-ov 6190 df-oprab 6191 df-poset 15215 df-plt 15227 df-lub 15243 df-glb 15244 df-join 15245 df-meet 15246 df-p0 15308 df-p1 15309 df-lat 15315 df-clat 15377 df-oposet 33124 df-ol 33126 df-oml 33127 df-covers 33214 df-ats 33215 df-atl 33246 df-cvlat 33270 df-hlat 33299 df-lhyp 33935 |
This theorem is referenced by: cdlemd4 34148 cdlemd9 34153 cdleme25a 34300 cdleme25c 34302 cdleme25dN 34303 cdleme26ee 34307 cdlemefs32sn1aw 34361 cdleme43fsv1snlem 34367 cdleme41sn3a 34380 cdleme40m 34414 cdleme40n 34415 cdleme17d3 34443 cdlemeg46gfre 34479 cdleme50trn2 34498 cdlemb3 34553 |
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