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Theorem iedgval3sn 26512
 Description: Degenerated case 3 for edges: The set of indexed edges of a singleton containing a singleton containing a singleton is the innermost singleton. (Contributed by AV, 24-Sep-2020.) (Avoid depending on this detail.)
Hypothesis
Ref Expression
vtxval3sn.a 𝐴 ∈ V
Assertion
Ref Expression
iedgval3sn (iEdg‘{{{𝐴}}}) = {𝐴}

Proof of Theorem iedgval3sn
StepHypRef Expression
1 vtxval3sn.a . 2 𝐴 ∈ V
21opid 4730 . . . 4 𝐴, 𝐴⟩ = {{𝐴}}
32eqcomi 2804 . . 3 {{𝐴}} = ⟨𝐴, 𝐴
43sneqi 4483 . 2 {{{𝐴}}} = {⟨𝐴, 𝐴⟩}
51, 4iedgvalsnop 26510 1 (iEdg‘{{{𝐴}}}) = {𝐴}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1522   ∈ wcel 2081  Vcvv 3437  {csn 4472  ⟨cop 4478  ‘cfv 6225  iEdgciedg 26465 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-10 2112  ax-11 2126  ax-12 2141  ax-13 2344  ax-ext 2769  ax-sep 5094  ax-nul 5101  ax-pow 5157  ax-pr 5221  ax-un 7319 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-3an 1082  df-tru 1525  df-ex 1762  df-nf 1766  df-sb 2043  df-mo 2576  df-eu 2612  df-clab 2776  df-cleq 2788  df-clel 2863  df-nfc 2935  df-ne 2985  df-ral 3110  df-rex 3111  df-rab 3114  df-v 3439  df-sbc 3707  df-dif 3862  df-un 3864  df-in 3866  df-ss 3874  df-nul 4212  df-if 4382  df-sn 4473  df-pr 4475  df-op 4479  df-uni 4746  df-br 4963  df-opab 5025  df-mpt 5042  df-id 5348  df-xp 5449  df-rel 5450  df-cnv 5451  df-co 5452  df-dm 5453  df-rn 5454  df-iota 6189  df-fun 6227  df-fv 6233  df-2nd 7546  df-iedg 26467 This theorem is referenced by: (None)
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