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Mirrors > Home > MPE Home > Th. List > fvresd | Structured version Visualization version GIF version |
Description: The value of a restricted function, deduction version of fvres 6207. (Contributed by Glauco Siliprandi, 8-Apr-2021.) |
Ref | Expression |
---|---|
fvresd.1 | ⊢ (𝜑 → 𝐴 ∈ 𝐵) |
Ref | Expression |
---|---|
fvresd | ⊢ (𝜑 → ((𝐹 ↾ 𝐵)‘𝐴) = (𝐹‘𝐴)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvresd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝐵) | |
2 | fvres 6207 | . 2 ⊢ (𝐴 ∈ 𝐵 → ((𝐹 ↾ 𝐵)‘𝐴) = (𝐹‘𝐴)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ((𝐹 ↾ 𝐵)‘𝐴) = (𝐹‘𝐴)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1483 ∈ wcel 1990 ↾ 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: ackbij2lem2 9062 cfsmolem 9092 txkgen 21455 loglesqrt 24499 uhgrspansubgrlem 26182 wlkres 26567 ftc2re 30676 reprsuc 30693 nolesgn2o 31824 nolesgn2ores 31825 noresle 31846 noprefixmo 31848 nosupres 31853 nosupbnd2lem1 31861 noetalem3 31865 limsupresxr 39998 liminfresxr 39999 sssmf 40947 |
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