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Mirrors > Home > MPE Home > Th. List > ushgruhgr | Structured version Visualization version Unicode version |
Description: An undirected simple hypergraph is an undirected hypergraph. (Contributed by AV, 19-Jan-2020.) (Revised by AV, 9-Oct-2020.) |
Ref | Expression |
---|---|
ushgruhgr | USHGraph UHGraph |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . . . 4 Vtx Vtx | |
2 | eqid 2622 | . . . 4 iEdg iEdg | |
3 | 1, 2 | ushgrf 25958 | . . 3 USHGraph iEdg iEdgVtx |
4 | f1f 6101 | . . 3 iEdg iEdgVtx iEdg iEdgVtx | |
5 | 3, 4 | syl 17 | . 2 USHGraph iEdg iEdgVtx |
6 | 1, 2 | isuhgr 25955 | . 2 USHGraph UHGraph iEdg iEdgVtx |
7 | 5, 6 | mpbird 247 | 1 USHGraph UHGraph |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cdif 3571 c0 3915 cpw 4158 csn 4177 cdm 5114 wf 5884 wf1 5885 cfv 5888 Vtxcvtx 25874 iEdgciedg 25875 UHGraph cuhgr 25951 USHGraph cushgr 25952 |
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-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fv 5896 df-uhgr 25953 df-ushgr 25954 |
This theorem is referenced by: ushgrun 25971 ushgrunop 25972 ushgredgedg 26121 ushgredgedgloop 26123 |
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