Theorem uspgruhgr 29594

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 29588	. 2 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UPGraph)
2		upgruhgr 29509	. 2 ⊢ (𝐺 ∈ UPGraph → 𝐺 ∈ UHGraph)
3	1, 2	syl 18	1 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2146  UHGraphcuhgr 29463  UPGraphcupgr 29487  USPGraphcuspgr 29558

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737  ax-nul 5271

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-ne 2961  df-rab 3419  df-v 3459  df-sbc 3747  df-dif 3909  df-un 3911  df-ss 3923  df-nul 4287  df-if 4490  df-pw 4566  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4875  df-br 5112  df-opab 5176  df-rel 5670  df-cnv 5671  df-co 5672  df-dm 5673  df-rn 5674  df-iota 6496  df-fun 6542  df-fn 6543  df-f 6544  df-f1 6545  df-fv 6548  df-uhgr 29465  df-upgr 29489  df-uspgr 29560

This theorem is used by:  isuspgrim0lem  48718  isuspgrim0  48719  isuspgrimlem  48720  isuspgrim  48721  upgrimwlklem2  48723  upgrimwlklem3  48724  upgrimtrlslem1  48729  upgrimtrlslem2  48730  grlimedgclnbgr  48820  grlimprclnbgr  48821  grlimprclnbgredg  48822  grlimgrtri  48828