Theorem uspgruhgr 29162

Description: An undirected simple pseudograph is an undirected hypergraph. (Contributed by AV, 21-Apr-2025.)

Assertion

Ref	Expression
uspgruhgr	⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

Proof of Theorem uspgruhgr

Step	Hyp	Ref	Expression
1		uspgrupgr 29156	. 2 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UPGraph)
2		upgruhgr 29080	. 2 ⊢ (𝐺 ∈ UPGraph → 𝐺 ∈ UHGraph)
3	1, 2	syl 17	1 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

Syntax hints:   → wi 4   ∈ wcel 2111  UHGraphcuhgr 29034  UPGraphcupgr 29058  USPGraphcuspgr 29126

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-nul 5242

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-ne 2929  df-rab 3396  df-v 3438  df-sbc 3737  df-dif 3900  df-un 3902  df-ss 3914  df-nul 4281  df-if 4473  df-pw 4549  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4857  df-br 5090  df-opab 5152  df-rel 5621  df-cnv 5622  df-co 5623  df-dm 5624  df-rn 5625  df-iota 6437  df-fun 6483  df-fn 6484  df-f 6485  df-f1 6486  df-fv 6489  df-uhgr 29036  df-upgr 29060  df-uspgr 29128

This theorem is referenced by:  isuspgrim0lem  48003  isuspgrim0  48004  isuspgrimlem  48005  isuspgrim  48006  upgrimwlklem2  48008  upgrimwlklem3  48009  upgrimtrlslem1  48014  upgrimtrlslem2  48015  grlimedgclnbgr  48105  grlimprclnbgr  48106  grlimprclnbgredg  48107  grlimgrtri  48113