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Mirrors > Home > MPE Home > Th. List > latasymb | Structured version Visualization version Unicode version |
Description: A lattice ordering is asymmetric. (eqss 3618 analog.) (Contributed by NM, 22-Oct-2011.) |
Ref | Expression |
---|---|
latref.b | |
latref.l |
Ref | Expression |
---|---|
latasymb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | latpos 17050 | . 2 | |
2 | latref.b | . . 3 | |
3 | latref.l | . . 3 | |
4 | 2, 3 | posasymb 16952 | . 2 |
5 | 1, 4 | syl3an1 1359 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 class class class wbr 4653 cfv 5888 cbs 15857 cple 15948 cpo 16940 clat 17045 |
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-nul 4789 |
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-dm 5124 df-iota 5851 df-fv 5896 df-preset 16928 df-poset 16946 df-lat 17046 |
This theorem is referenced by: latasym 17055 latasymd 17057 lubun 17123 cmtbr4N 34542 cvlexchb1 34617 hlateq 34685 cvratlem 34707 cvrat3 34728 pmap11 35048 cdleme50eq 35829 dia11N 36337 dib11N 36449 dih11 36554 |
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