Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > 2atjlej | Structured version Visualization version Unicode version |
Description: Two atoms are different if their join majorizes the join of two different atoms. (Contributed by NM, 4-Jun-2013.) |
Ref | Expression |
---|---|
ps1.l | |
ps1.j | |
ps1.a |
Ref | Expression |
---|---|
2atjlej |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp33 1099 | . . . 4 | |
2 | simp1 1061 | . . . . 5 | |
3 | simp21 1094 | . . . . 5 | |
4 | simp22 1095 | . . . . 5 | |
5 | simp23 1096 | . . . . 5 | |
6 | simp31 1097 | . . . . 5 | |
7 | simp32 1098 | . . . . 5 | |
8 | ps1.l | . . . . . 6 | |
9 | ps1.j | . . . . . 6 | |
10 | ps1.a | . . . . . 6 | |
11 | 8, 9, 10 | ps-1 34763 | . . . . 5 |
12 | 2, 3, 4, 5, 6, 7, 11 | syl132anc 1344 | . . . 4 |
13 | 1, 12 | mpbid 222 | . . 3 |
14 | 9, 10 | lnnat 34713 | . . . . 5 |
15 | 2, 3, 4, 14 | syl3anc 1326 | . . . 4 |
16 | 5, 15 | mpbid 222 | . . 3 |
17 | 13, 16 | eqneltrrd 2721 | . 2 |
18 | 9, 10 | lnnat 34713 | . . 3 |
19 | 2, 6, 7, 18 | syl3anc 1326 | . 2 |
20 | 17, 19 | mpbird 247 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 w3a 1037 wceq 1483 wcel 1990 wne 2794 class class class wbr 4653 cfv 5888 (class class class)co 6650 cple 15948 cjn 16944 catm 34550 chlt 34637 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-oprab 6654 df-preset 16928 df-poset 16946 df-plt 16958 df-lub 16974 df-glb 16975 df-join 16976 df-meet 16977 df-p0 17039 df-lat 17046 df-clat 17108 df-oposet 34463 df-ol 34465 df-oml 34466 df-covers 34553 df-ats 34554 df-atl 34585 df-cvlat 34609 df-hlat 34638 |
This theorem is referenced by: cdlemg46 36023 |
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