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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > afvprc | Structured version Visualization version GIF version |
Description: A function's value at a proper class is the universe, compare with fvprc 6884. (Contributed by Alexander van der Vekens, 25-May-2017.) |
Ref | Expression |
---|---|
afvprc | ⊢ (¬ 𝐴 ∈ V → (𝐹'''𝐴) = V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prcnel 3496 | . 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹) | |
2 | ndmafv 46148 | . 2 ⊢ (¬ 𝐴 ∈ dom 𝐹 → (𝐹'''𝐴) = V) | |
3 | 1, 2 | syl 17 | 1 ⊢ (¬ 𝐴 ∈ V → (𝐹'''𝐴) = V) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 = wceq 1539 ∈ wcel 2104 Vcvv 3472 dom cdm 5677 '''cafv 46125 |
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 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5300 ax-nul 5307 ax-pr 5428 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 844 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-ral 3060 df-rex 3069 df-rab 3431 df-v 3474 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-int 4952 df-br 5150 df-opab 5212 df-id 5575 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-res 5689 df-iota 6496 df-fun 6546 df-fv 6552 df-aiota 46093 df-dfat 46127 df-afv 46128 |
This theorem is referenced by: afvvv 46153 |
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