Theorem uspgruhgr 29385

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 29379	. 2 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UPGraph)
2		upgruhgr 29303	. 2 ⊢ (𝐺 ∈ UPGraph → 𝐺 ∈ UHGraph)
3	1, 2	syl 17	1 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

Syntax hints:   → wi 4   ∈ wcel 2142  UHGraphcuhgr 29257  UPGraphcupgr 29281  USPGraphcuspgr 29349

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734  ax-nul 5256

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1100  df-tru 1563  df-fal 1573  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-ne 2958  df-rab 3415  df-v 3456  df-sbc 3745  df-dif 3907  df-un 3909  df-ss 3921  df-nul 4286  df-if 4481  df-pw 4557  df-sn 4583  df-pr 4585  df-op 4589  df-uni 4866  df-br 5101  df-opab 5163  df-rel 5654  df-cnv 5655  df-co 5656  df-dm 5657  df-rn 5658  df-iota 6477  df-fun 6523  df-fn 6524  df-f 6525  df-f1 6526  df-fv 6529  df-uhgr 29259  df-upgr 29283  df-uspgr 29351

This theorem is referenced by:  isuspgrim0lem  48515  isuspgrim0  48516  isuspgrimlem  48517  isuspgrim  48518  upgrimwlklem2  48520  upgrimwlklem3  48521  upgrimtrlslem1  48526  upgrimtrlslem2  48527  grlimedgclnbgr  48617  grlimprclnbgr  48618  grlimprclnbgredg  48619  grlimgrtri  48625