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Theorem cusgrusgr 29456
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 29455 . 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 2108  USGraphcusgr 29186  ComplGraphccplgr 29446  ComplUSGraphccusgr 29447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-in 3983  df-cusgr 29449
This theorem is referenced by:  cusgrres  29486  cusgrsizeindslem  29489  cusgrsizeinds  29490  cusgrsize  29492  cusgrrusgr  29619  cusgredgex  35091  cusgr3cyclex  35106  cusgracyclt3v  35126
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