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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > fexafv2ex | Structured version Visualization version GIF version |
Description: The alternate function value is always a set if the function (resp. the domain of the function) is a set. (Contributed by AV, 3-Sep-2022.) |
Ref | Expression |
---|---|
fexafv2ex | ⊢ (𝐹 ∈ 𝑉 → (𝐹''''𝐴) ∈ V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rnexg 7360 | . 2 ⊢ (𝐹 ∈ 𝑉 → ran 𝐹 ∈ V) | |
2 | afv2ex 42117 | . 2 ⊢ (ran 𝐹 ∈ V → (𝐹''''𝐴) ∈ V) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝐹 ∈ 𝑉 → (𝐹''''𝐴) ∈ V) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2166 Vcvv 3415 ran crn 5344 ''''cafv2 42111 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-8 2168 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-13 2391 ax-ext 2804 ax-sep 5006 ax-nul 5014 ax-pow 5066 ax-pr 5128 ax-un 7210 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-3an 1115 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-mo 2606 df-eu 2641 df-clab 2813 df-cleq 2819 df-clel 2822 df-nfc 2959 df-ral 3123 df-rex 3124 df-rab 3127 df-v 3417 df-sbc 3664 df-dif 3802 df-un 3804 df-in 3806 df-ss 3813 df-nul 4146 df-if 4308 df-pw 4381 df-sn 4399 df-pr 4401 df-op 4405 df-uni 4660 df-br 4875 df-opab 4937 df-cnv 5351 df-dm 5353 df-rn 5354 df-iota 6087 df-afv2 42112 |
This theorem is referenced by: (None) |
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