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Theorem usgfislem1 40264
 Description: Lemma 1 for usgfis 40266: The set of edges is the union of the edges containing a specific vertex and the edges not containing this vertex. (Contributed by Alexander van der Vekens, 4-Jan-2018.) (Revised by AV, 10-Jan-2020.)
Hypotheses
Ref Expression
usgresvm1.v VtxALTV
usgresvm1.e Edges
usgresvm1.f
Assertion
Ref Expression
usgfislem1
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem usgfislem1
StepHypRef Expression
1 df-nel 2644 . . . . . 6
21bicomi 207 . . . . 5
32a1i 11 . . . 4
43rabbiia 3019 . . 3
54uneq1i 3575 . 2
6 rabxm 3758 . . 3
76equncomi 3571 . 2
8 usgresvm1.f . . 3
98uneq1i 3575 . 2
105, 7, 93eqtr4i 2503 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 189   wceq 1452   wcel 1904   wnel 2642  crab 2760   cun 3388  cfv 5589   Edges cedg 25137   VtxALTV cvtxaltv 40201 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-nel 2644  df-ral 2761  df-rab 2765  df-v 3033  df-un 3395 This theorem is referenced by:  usgfislem2  40265
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