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Mirrors > Home > MPE Home > Th. List > fvressn | Structured version Visualization version GIF version |
Description: The value of a function restricted to the singleton containing the argument equals the value of the function for this argument. (Contributed by Alexander van der Vekens, 22-Jul-2018.) |
Ref | Expression |
---|---|
fvressn | ⊢ (𝑋 ∈ 𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹‘𝑋)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg 4206 | . 2 ⊢ (𝑋 ∈ 𝑉 → 𝑋 ∈ {𝑋}) | |
2 | fvres 6207 | . 2 ⊢ (𝑋 ∈ {𝑋} → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹‘𝑋)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝑋 ∈ 𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹‘𝑋)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1483 ∈ wcel 1990 {csn 4177 ↾ cres 5116 ‘cfv 5888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-res 5126 df-iota 5851 df-fv 5896 |
This theorem is referenced by: fvn0fvelrn 6430 fvunsn 6445 |
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