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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > hlatexch2 | Structured version Visualization version Unicode version |
Description: Atom exchange property. (Contributed by NM, 8-Jan-2012.) |
Ref | Expression |
---|---|
hlatexchb.l |
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hlatexchb.j |
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hlatexchb.a |
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Ref | Expression |
---|---|
hlatexch2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlcvl 32925 |
. 2
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2 | hlatexchb.l |
. . 3
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3 | hlatexchb.j |
. . 3
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4 | hlatexchb.a |
. . 3
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5 | 2, 3, 4 | cvlatexch2 32903 |
. 2
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6 | 1, 5 | syl3an1 1301 |
1
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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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-rep 4515 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-iun 4280 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-riota 6252 df-ov 6293 df-oprab 6294 df-preset 16173 df-poset 16191 df-plt 16204 df-lub 16220 df-glb 16221 df-join 16222 df-meet 16223 df-p0 16285 df-lat 16292 df-covers 32832 df-ats 32833 df-atl 32864 df-cvlat 32888 df-hlat 32917 |
This theorem is referenced by: 2llnneN 32974 atexchcvrN 33005 atbtwnex 33013 3dimlem3 33026 3dimlem3OLDN 33027 3dimlem4 33029 3dimlem4OLDN 33030 hlatexch4 33046 3atlem5 33052 dalem27 33264 cdlemblem 33358 paddasslem1 33385 paddasslem6 33390 cdleme3g 33800 cdleme3h 33801 cdleme7d 33812 cdleme11c 33827 cdleme11dN 33828 cdleme36a 34027 cdlemeg46rgv 34095 cdlemk14 34421 dia2dimlem1 34632 dia2dimlem2 34633 dia2dimlem3 34634 |
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