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Theorem iedgval0 26836
Description: Degenerated case 1 for edges: The set of indexed edges of the empty set is the empty set. (Contributed by AV, 24-Sep-2020.)
Assertion
Ref Expression
iedgval0 (iEdg‘∅) = ∅

Proof of Theorem iedgval0
StepHypRef Expression
1 0nelxp 5557 . . 3 ¬ ∅ ∈ (V × V)
21iffalsei 4438 . 2 if(∅ ∈ (V × V), (2nd ‘∅), (.ef‘∅)) = (.ef‘∅)
3 iedgval 26797 . 2 (iEdg‘∅) = if(∅ ∈ (V × V), (2nd ‘∅), (.ef‘∅))
4 df-edgf 26786 . . 3 .ef = Slot 18
54str0 16530 . 2 ∅ = (.ef‘∅)
62, 3, 53eqtr4i 2834 1 (iEdg‘∅) = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  wcel 2112  Vcvv 3444  c0 4246  ifcif 4428   × cxp 5521  cfv 6328  2nd c2nd 7674  1c1 10531  8c8 11690  cdc 12090  .efcedgf 26785  iEdgciedg 26793
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-sep 5170  ax-nul 5177  ax-pow 5234  ax-pr 5298
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2601  df-eu 2632  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ne 2991  df-ral 3114  df-rex 3115  df-rab 3118  df-v 3446  df-sbc 3724  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-opab 5096  df-mpt 5114  df-id 5428  df-xp 5529  df-rel 5530  df-cnv 5531  df-co 5532  df-dm 5533  df-iota 6287  df-fun 6330  df-fv 6336  df-slot 16482  df-edgf 26786  df-iedg 26795
This theorem is referenced by:  uhgr0  26869  usgr0  27036  0grsubgr  27071  0grrusgr  27372
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