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Theorem cusgrcplgr 29452
Description: A complete simple graph is a complete graph. (Contributed by AV, 1-Nov-2020.)
Assertion
Ref Expression
cusgrcplgr (𝐺 ∈ ComplUSGraph → 𝐺 ∈ ComplGraph)

Proof of Theorem cusgrcplgr
StepHypRef Expression
1 iscusgr 29450 . 2 (𝐺 ∈ ComplUSGraph ↔ (𝐺 ∈ USGraph ∧ 𝐺 ∈ ComplGraph))
21simprbi 496 1 (𝐺 ∈ ComplUSGraph → 𝐺 ∈ ComplGraph)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  USGraphcusgr 29181  ComplGraphccplgr 29441  ComplUSGraphccusgr 29442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-in 3970  df-cusgr 29444
This theorem is referenced by:  cusgrsizeindslem  29484  cusgrrusgr  29614  cusgredgex  35106
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