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Mirrors > Home > MPE Home > Th. List > slotfn | Structured version Visualization version GIF version |
Description: A slot is a function on sets, treated as structures. (Contributed by Mario Carneiro, 22-Sep-2015.) |
Ref | Expression |
---|---|
strfvnd.c | ⊢ 𝐸 = Slot 𝑁 |
Ref | Expression |
---|---|
slotfn | ⊢ 𝐸 Fn V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvex 6894 | . 2 ⊢ (𝑥‘𝑁) ∈ V | |
2 | strfvnd.c | . . 3 ⊢ 𝐸 = Slot 𝑁 | |
3 | df-slot 17114 | . . 3 ⊢ Slot 𝑁 = (𝑥 ∈ V ↦ (𝑥‘𝑁)) | |
4 | 2, 3 | eqtri 2752 | . 2 ⊢ 𝐸 = (𝑥 ∈ V ↦ (𝑥‘𝑁)) |
5 | 1, 4 | fnmpti 6683 | 1 ⊢ 𝐸 Fn V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 Vcvv 3466 ↦ cmpt 5221 Fn wfn 6528 ‘cfv 6533 Slot cslot 17113 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2695 ax-sep 5289 ax-nul 5296 ax-pr 5417 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2526 df-eu 2555 df-clab 2702 df-cleq 2716 df-clel 2802 df-nfc 2877 df-ne 2933 df-ral 3054 df-rex 3063 df-rab 3425 df-v 3468 df-dif 3943 df-un 3945 df-in 3947 df-ss 3957 df-nul 4315 df-if 4521 df-sn 4621 df-pr 4623 df-op 4627 df-uni 4900 df-br 5139 df-opab 5201 df-mpt 5222 df-id 5564 df-xp 5672 df-rel 5673 df-cnv 5674 df-co 5675 df-dm 5676 df-iota 6485 df-fun 6535 df-fn 6536 df-fv 6541 df-slot 17114 |
This theorem is referenced by: basfn 17147 bj-isrvec 36665 |
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