![]() |
Mathbox for Alexander van der Vekens |
< Previous
Next >
Nearby theorems |
|
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 6896. (Contributed by Alexander van der Vekens, 25-May-2017.) |
Ref | Expression |
---|---|
afvprc | ⊢ (¬ 𝐴 ∈ V → (𝐹'''𝐴) = V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prcnel 3506 | . 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹) | |
2 | ndmafv 47125 | . 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 1540 ∈ wcel 2108 Vcvv 3479 dom cdm 5683 '''cafv 47102 |
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 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2707 ax-sep 5294 ax-nul 5304 ax-pr 5430 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2539 df-eu 2568 df-clab 2714 df-cleq 2728 df-clel 2815 df-nfc 2891 df-ne 2940 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-sbc 3788 df-csb 3899 df-dif 3953 df-un 3955 df-in 3957 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4906 df-int 4945 df-br 5142 df-opab 5204 df-id 5576 df-xp 5689 df-rel 5690 df-cnv 5691 df-co 5692 df-dm 5693 df-res 5695 df-iota 6512 df-fun 6561 df-fv 6567 df-aiota 47070 df-dfat 47104 df-afv 47105 |
This theorem is referenced by: afvvv 47130 |
Copyright terms: Public domain | W3C validator |