Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > posrasymb | Structured version Visualization version Unicode version |
Description: A poset ordering is asymetric. (Contributed by Thierry Arnoux, 13-Sep-2018.) |
Ref | Expression |
---|---|
posrasymb.b | |
posrasymb.l |
Ref | Expression |
---|---|
posrasymb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | posrasymb.l | . . . . 5 | |
2 | 1 | breqi 4659 | . . . 4 |
3 | simp2 1062 | . . . . . 6 | |
4 | simp3 1063 | . . . . . 6 | |
5 | brxp 5147 | . . . . . 6 | |
6 | 3, 4, 5 | sylanbrc 698 | . . . . 5 |
7 | brin 4704 | . . . . . 6 | |
8 | 7 | rbaib 947 | . . . . 5 |
9 | 6, 8 | syl 17 | . . . 4 |
10 | 2, 9 | syl5bb 272 | . . 3 |
11 | 1 | breqi 4659 | . . . 4 |
12 | brxp 5147 | . . . . . 6 | |
13 | 4, 3, 12 | sylanbrc 698 | . . . . 5 |
14 | brin 4704 | . . . . . 6 | |
15 | 14 | rbaib 947 | . . . . 5 |
16 | 13, 15 | syl 17 | . . . 4 |
17 | 11, 16 | syl5bb 272 | . . 3 |
18 | 10, 17 | anbi12d 747 | . 2 |
19 | posrasymb.b | . . 3 | |
20 | eqid 2622 | . . 3 | |
21 | 19, 20 | posasymb 16952 | . 2 |
22 | 18, 21 | bitrd 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 cin 3573 class class class wbr 4653 cxp 5112 cfv 5888 cbs 15857 cple 15948 cpo 16940 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-iota 5851 df-fv 5896 df-preset 16928 df-poset 16946 |
This theorem is referenced by: ordtconnlem1 29970 |
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