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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > afv2prc | Structured version Visualization version GIF version |
Description: A function's value at a proper class is not defined, compare with fvprc 6638. (Contributed by AV, 5-Sep-2022.) |
Ref | Expression |
---|---|
afv2prc | ⊢ (¬ 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prcnel 3465 | . 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹) | |
2 | ndmafv2nrn 43778 | . 2 ⊢ (¬ 𝐴 ∈ dom 𝐹 → (𝐹''''𝐴) ∉ ran 𝐹) | |
3 | 1, 2 | syl 17 | 1 ⊢ (¬ 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∈ wcel 2111 ∉ wnel 3091 Vcvv 3441 dom cdm 5519 ran crn 5520 ''''cafv2 43764 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pr 5295 ax-un 7441 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-nel 3092 df-rab 3115 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-pw 4499 df-sn 4526 df-pr 4528 df-uni 4801 df-dfat 43675 df-afv2 43765 |
This theorem is referenced by: (None) |
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