![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 4559 | . 2 ⊢ (𝑋 ∈ 𝑉 → 𝑋 ∈ {𝑋}) | |
2 | 1 | fvresd 6665 | 1 ⊢ (𝑋 ∈ 𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹‘𝑋)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1538 ∈ wcel 2111 {csn 4525 ↾ cres 5521 ‘cfv 6324 |
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 |
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-ral 3111 df-rex 3112 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-uni 4801 df-br 5031 df-opab 5093 df-xp 5525 df-res 5531 df-iota 6283 df-fv 6332 |
This theorem is referenced by: fvn0fvelrn 6902 fvunsn 6918 funressndmfvrn 43636 |
Copyright terms: Public domain | W3C validator |