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Mirrors > Home > MPE Home > Th. List > trlsegvdeglem2 | Structured version Visualization version Unicode version |
Description: Lemma for trlsegvdeg 27087. (Contributed by AV, 20-Feb-2021.) |
Ref | Expression |
---|---|
trlsegvdeg.v | Vtx |
trlsegvdeg.i | iEdg |
trlsegvdeg.f | |
trlsegvdeg.n | ..^ |
trlsegvdeg.u | |
trlsegvdeg.w | Trails |
trlsegvdeg.vx | Vtx |
trlsegvdeg.vy | Vtx |
trlsegvdeg.vz | Vtx |
trlsegvdeg.ix | iEdg ..^ |
trlsegvdeg.iy | iEdg |
trlsegvdeg.iz | iEdg |
Ref | Expression |
---|---|
trlsegvdeglem2 | iEdg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | trlsegvdeg.f | . . 3 | |
2 | funres 5929 | . . 3 ..^ | |
3 | 1, 2 | syl 17 | . 2 ..^ |
4 | trlsegvdeg.ix | . . 3 iEdg ..^ | |
5 | 4 | funeqd 5910 | . 2 iEdg ..^ |
6 | 3, 5 | mpbird 247 | 1 iEdg |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 csn 4177 cop 4183 class class class wbr 4653 cres 5116 cima 5117 wfun 5882 cfv 5888 (class class class)co 6650 cc0 9936 cfz 12326 ..^cfzo 12465 chash 13117 Vtxcvtx 25874 iEdgciedg 25875 Trailsctrls 26587 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ss 3588 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-res 5126 df-fun 5890 |
This theorem is referenced by: trlsegvdeg 27087 |
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