Theorem uspgruhgr 29647

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 29641	. 2 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UPGraph)
2		upgruhgr 29562	. 2 ⊢ (𝐺 ∈ UPGraph → 𝐺 ∈ UHGraph)
3	1, 2	syl 18	1 ⊢ (𝐺 ∈ USPGraph → 𝐺 ∈ UHGraph)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145  UHGraphcuhgr 29516  UPGraphcupgr 29540  USPGraphcuspgr 29611

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 2147  ax-9 2155  ax-ext 2732  ax-nul 5263

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 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-rab 3413  df-v 3452  df-sbc 3740  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4280  df-if 4483  df-pw 4559  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4868  df-br 5104  df-opab 5168  df-rel 5662  df-cnv 5663  df-co 5664  df-dm 5665  df-rn 5666  df-iota 6489  df-fun 6535  df-fn 6536  df-f 6537  df-f1 6538  df-fv 6541  df-uhgr 29518  df-upgr 29542  df-uspgr 29613

This theorem is used by:  isuspgrim0lem  48812  isuspgrim0  48813  isuspgrimlem  48814  isuspgrim  48815  upgrimwlklem2  48817  upgrimwlklem3  48818  upgrimtrlslem1  48823  upgrimtrlslem2  48824  grlimedgclnbgr  48914  grlimprclnbgr  48915  grlimprclnbgredg  48916  grlimgrtri  48922