Theorem wksv 29523

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 6853	. 2 ⊢ (Walks‘𝐺) ∈ V
2		opabss 5166	. 2 ⊢ {⟨𝑓, 𝑝⟩ ∣ 𝑓(Walks‘𝐺)𝑝} ⊆ (Walks‘𝐺)
3	1, 2	ssexi 5272	1 ⊢ {⟨𝑓, 𝑝⟩ ∣ 𝑓(Walks‘𝐺)𝑝} ∈ V

Syntax hints:   ∈ wcel 2109  Vcvv 3444   class class class wbr 5102  {copab 5164  ‘cfv 6499  Walkscwlks 29500

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5246  ax-nul 5256

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ne 2926  df-rab 3403  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4293  df-sn 4586  df-pr 4588  df-uni 4868  df-br 5103  df-opab 5165  df-iota 6452  df-fv 6507

This theorem is referenced by: (None)