Theorem uspgruhgr 29471

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 29465	. 2 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UPGraph)
2		upgruhgr 29389	. 2 ⊢ (𝐺 ∈ UPGraph → 𝐺 ∈ UHGraph)
3	1, 2	syl 18	1 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

Syntax hints:   → wi 4   ∈ wcel 2149  UHGraphcuhgr 29343  UPGraphcupgr 29367  USPGraphcuspgr 29435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-nul 5268

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-ne 2965  df-rab 3424  df-v 3465  df-sbc 3754  df-dif 3916  df-un 3918  df-ss 3930  df-nul 4295  df-if 4490  df-pw 4566  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4874  df-br 5111  df-opab 5175  df-rel 5666  df-cnv 5667  df-co 5668  df-dm 5669  df-rn 5670  df-iota 6490  df-fun 6536  df-fn 6537  df-f 6538  df-f1 6539  df-fv 6542  df-uhgr 29345  df-upgr 29369  df-uspgr 29437

This theorem is referenced by:  isuspgrim0lem  48542  isuspgrim0  48543  isuspgrimlem  48544  isuspgrim  48545  upgrimwlklem2  48547  upgrimwlklem3  48548  upgrimtrlslem1  48553  upgrimtrlslem2  48554  grlimedgclnbgr  48644  grlimprclnbgr  48645  grlimprclnbgredg  48646  grlimgrtri  48652