Theorem wksv 29598

Description: The class of walks is a set. (Contributed by AV, 15-Jan-2021.) (Proof shortened by SN, 11-Dec-2024.)

Assertion

Ref	Expression
wksv	⊢ {⟨𝑓, 𝑝⟩ ∣ 𝑓(Walks‘𝐺)𝑝} ∈ V

Distinct variable group:   𝑓,𝐺,𝑝

Proof of Theorem wksv

Step	Hyp	Ref	Expression
1		fvex 6835	. 2 ⊢ (Walks‘𝐺) ∈ V
2		opabss 5153	. 2 ⊢ {⟨𝑓, 𝑝⟩ ∣ 𝑓(Walks‘𝐺)𝑝} ⊆ (Walks‘𝐺)
3	1, 2	ssexi 5258	1 ⊢ {⟨𝑓, 𝑝⟩ ∣ 𝑓(Walks‘𝐺)𝑝} ∈ V

Syntax hints:   ∈ wcel 2111  Vcvv 3436   class class class wbr 5089  {copab 5151  ‘cfv 6481  Walkscwlks 29575

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-sep 5232  ax-nul 5242

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-ne 2929  df-rab 3396  df-v 3438  df-dif 3900  df-un 3902  df-in 3904  df-ss 3914  df-nul 4281  df-sn 4574  df-pr 4576  df-uni 4857  df-br 5090  df-opab 5152  df-iota 6437  df-fv 6489

This theorem is referenced by: (None)