Theorem wksv 29709

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 6851	. 2 ⊢ (Walks‘𝐺) ∈ V
2		opabss 5150	. 2 ⊢ {⟨𝑓, 𝑝⟩ ∣ 𝑓(Walks‘𝐺)𝑝} ⊆ (Walks‘𝐺)
3	1, 2	ssexi 5262	1 ⊢ {⟨𝑓, 𝑝⟩ ∣ 𝑓(Walks‘𝐺)𝑝} ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3430   class class class wbr 5086  {copab 5148  ‘cfv 6496  Walkscwlks 29686

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5232  ax-nul 5242

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4275  df-sn 4569  df-pr 4571  df-uni 4852  df-br 5087  df-opab 5149  df-iota 6452  df-fv 6504

This theorem is referenced by: (None)