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Theorem cusgrusgr 29184
Description: A complete simple graph is a simple graph. (Contributed by Alexander van der Vekens, 13-Oct-2017.) (Revised by AV, 1-Nov-2020.)
Assertion
Ref Expression
cusgrusgr (𝐺 ∈ ComplUSGraph → 𝐺 ∈ USGraph)

Proof of Theorem cusgrusgr
StepHypRef Expression
1 iscusgr 29183 . 2 (𝐺 ∈ ComplUSGraph ↔ (𝐺 ∈ USGraph ∧ 𝐺 ∈ ComplGraph))
21simplbi 497 1 (𝐺 ∈ ComplUSGraph → 𝐺 ∈ USGraph)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  USGraphcusgr 28917  ComplGraphccplgr 29174  ComplUSGraphccusgr 29175
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-in 3950  df-cusgr 29177
This theorem is referenced by:  cusgrres  29214  cusgrsizeindslem  29217  cusgrsizeinds  29218  cusgrsize  29220  cusgrrusgr  29347  cusgredgex  34640  cusgr3cyclex  34655  cusgracyclt3v  34675
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