Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemd | Structured version Visualization version Unicode version |
Description: If two translations agree at any atom not under the fiducial co-atom , then they are equal. Lemma D in [Crawley] p. 113. (Contributed by NM, 2-Jun-2012.) |
Ref | Expression |
---|---|
cdlemd.l | |
cdlemd.a | |
cdlemd.h | |
cdlemd.t |
Ref | Expression |
---|---|
cdlemd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl11 1136 | . . . 4 | |
2 | simpl12 1137 | . . . . 5 | |
3 | simpl13 1138 | . . . . 5 | |
4 | 2, 3 | jca 554 | . . . 4 |
5 | simpr 477 | . . . 4 | |
6 | simpl2 1065 | . . . 4 | |
7 | simpl3 1066 | . . . 4 | |
8 | cdlemd.l | . . . . 5 | |
9 | eqid 2622 | . . . . 5 | |
10 | cdlemd.a | . . . . 5 | |
11 | cdlemd.h | . . . . 5 | |
12 | cdlemd.t | . . . . 5 | |
13 | 8, 9, 10, 11, 12 | cdlemd9 35493 | . . . 4 |
14 | 1, 4, 5, 6, 7, 13 | syl311anc 1340 | . . 3 |
15 | 14 | ralrimiva 2966 | . 2 |
16 | 10, 11, 12 | ltrneq2 35434 | . . 3 |
17 | 16 | 3ad2ant1 1082 | . 2 |
18 | 15, 17 | mpbid 222 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 wral 2912 class class class wbr 4653 cfv 5888 cple 15948 cjn 16944 catm 34550 chlt 34637 clh 35270 cltrn 35387 |
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-iin 4523 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-mpt2 6655 df-1st 7168 df-2nd 7169 df-map 7859 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-p1 17040 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 df-llines 34784 df-psubsp 34789 df-pmap 34790 df-padd 35082 df-lhyp 35274 df-laut 35275 df-ldil 35390 df-ltrn 35391 df-trl 35446 |
This theorem is referenced by: ltrneq3 35495 cdleme 35848 cdlemg1a 35858 ltrniotavalbN 35872 cdlemg44 36021 cdlemk19 36157 cdlemk27-3 36195 cdlemk33N 36197 cdlemk34 36198 cdlemk53a 36243 cdlemk19u 36258 dia2dimlem4 36356 dih1dimatlem0 36617 |
Copyright terms: Public domain | W3C validator |