Theorem uspgruhgr 29129

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 29123	. 2 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UPGraph)
2		upgruhgr 29047	. 2 ⊢ (𝐺 ∈ UPGraph → 𝐺 ∈ UHGraph)
3	1, 2	syl 17	1 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

Syntax hints:   → wi 4   ∈ wcel 2109  UHGraphcuhgr 29001  UPGraphcupgr 29025  USPGraphcuspgr 29093

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 2701  ax-nul 5245

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ne 2926  df-rab 3395  df-v 3438  df-sbc 3743  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4285  df-if 4477  df-pw 4553  df-sn 4578  df-pr 4580  df-op 4584  df-uni 4859  df-br 5093  df-opab 5155  df-rel 5626  df-cnv 5627  df-co 5628  df-dm 5629  df-rn 5630  df-iota 6438  df-fun 6484  df-fn 6485  df-f 6486  df-f1 6487  df-fv 6490  df-uhgr 29003  df-upgr 29027  df-uspgr 29095

This theorem is referenced by:  isuspgrim0lem  47881  isuspgrim0  47882  isuspgrimlem  47883  isuspgrim  47884  upgrimwlklem2  47886  upgrimwlklem3  47887  upgrimtrlslem1  47892  upgrimtrlslem2  47893  grlimedgclnbgr  47983  grlimprclnbgr  47984  grlimprclnbgredg  47985  grlimgrtri  47991