Theorem cusgrcplgr 29353

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

Step	Hyp	Ref	Expression
1		iscusgr 29351	. 2 ⊢ (𝐺 ∈ ComplUSGraph ↔ (𝐺 ∈ USGraph ∧ 𝐺 ∈ ComplGraph))
2	1	simprbi 496	1 ⊢ (𝐺 ∈ ComplUSGraph → 𝐺 ∈ ComplGraph)

Syntax hints:   → wi 4   ∈ wcel 2109  USGraphcusgr 29082  ComplGraphccplgr 29342  ComplUSGraphccusgr 29343

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-in 3923  df-cusgr 29345

This theorem is referenced by:  cusgrsizeindslem  29385  cusgrrusgr  29515  cusgredgex  35109