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Mirrors > Home > MPE Home > Th. List > wksv | Structured version Visualization version GIF version |
Description: The class of walks is a set. (Contributed by AV, 15-Jan-2021.) (Proof shortened by SN, 11-Dec-2024.) |
Ref | Expression |
---|---|
wksv | ⊢ {〈𝑓, 𝑝〉 ∣ 𝑓(Walks‘𝐺)𝑝} ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvex 6914 | . 2 ⊢ (Walks‘𝐺) ∈ V | |
2 | opabss 5217 | . 2 ⊢ {〈𝑓, 𝑝〉 ∣ 𝑓(Walks‘𝐺)𝑝} ⊆ (Walks‘𝐺) | |
3 | 1, 2 | ssexi 5327 | 1 ⊢ {〈𝑓, 𝑝〉 ∣ 𝑓(Walks‘𝐺)𝑝} ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2099 Vcvv 3462 class class class wbr 5153 {copab 5215 ‘cfv 6554 Walkscwlks 29533 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2697 ax-sep 5304 ax-nul 5311 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2704 df-cleq 2718 df-clel 2803 df-ne 2931 df-rab 3420 df-v 3464 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4326 df-sn 4634 df-pr 4636 df-uni 4914 df-br 5154 df-opab 5216 df-iota 6506 df-fv 6562 |
This theorem is referenced by: wlkResOLD 29587 wksonproplemOLD 29642 |
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