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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 6893. (Contributed by Alexander van der Vekens, 25-May-2017.) |
Ref | Expression |
---|---|
afvprc | ⊢ (¬ 𝐴 ∈ V → (𝐹'''𝐴) = V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prcnel 3504 | . 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹) | |
2 | ndmafv 47040 | . 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 1535 ∈ wcel 2104 Vcvv 3477 dom cdm 5683 '''cafv 47017 |
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 1963 ax-7 2003 ax-8 2106 ax-9 2114 ax-10 2137 ax-11 2153 ax-12 2173 ax-ext 2704 ax-sep 5300 ax-nul 5307 ax-pr 5430 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-3an 1087 df-tru 1538 df-fal 1548 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2536 df-eu 2565 df-clab 2711 df-cleq 2725 df-clel 2812 df-nfc 2888 df-ne 2937 df-ral 3058 df-rex 3067 df-rab 3433 df-v 3479 df-sbc 3792 df-csb 3909 df-dif 3966 df-un 3968 df-in 3970 df-ss 3980 df-nul 4340 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-uni 4915 df-int 4954 df-br 5150 df-opab 5212 df-id 5576 df-xp 5689 df-rel 5690 df-cnv 5691 df-co 5692 df-dm 5693 df-res 5695 df-iota 6510 df-fun 6560 df-fv 6566 df-aiota 46985 df-dfat 47019 df-afv 47020 |
This theorem is referenced by: afvvv 47045 |
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