Theorem uspgruhgr 29822

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 29816	. 2 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UPGraph)
2		upgruhgr 29737	. 2 ⊢ (𝐺 ∈ UPGraph → 𝐺 ∈ UHGraph)
3	1, 2	syl 18	1 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2147  UHGraphcuhgr 29691  UPGraphcupgr 29715  USPGraphcuspgr 29786

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-nul 5266

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 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-ne 2960  df-rab 3417  df-v 3456  df-sbc 3743  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-if 4486  df-pw 4562  df-sn 4589  df-pr 4591  df-op 4841  df-uni 4873  df-br 5109  df-opab 5174  df-rel 5665  df-cnv 5666  df-co 5667  df-dm 5668  df-rn 5669  df-iota 6520  df-fun 6568  df-fn 6569  df-f 6570  df-f1 6571  df-fv 6574  df-uhgr 29693  df-upgr 29717  df-uspgr 29788

This theorem is used by:  isuspgrim0lem  49264  isuspgrim0  49265  isuspgrimlem  49266  isuspgrim  49267  upgrimwlklem2  49269  upgrimwlklem3  49270  upgrimtrlslem1  49275  upgrimtrlslem2  49276  grlimedgclnbgr  49366  grlimprclnbgr  49367  grlimprclnbgredg  49368  grlimgrtri  49374