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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-evalfn | Structured version Visualization version GIF version |
Description: The evaluation at a class is a function on the universal class. (General form of slotfn 16504). (Contributed by Mario Carneiro, 22-Sep-2015.) (Revised by BJ, 27-Dec-2021.) |
Ref | Expression |
---|---|
bj-evalfn | ⊢ Slot 𝐴 Fn V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvex 6686 | . 2 ⊢ (𝑓‘𝐴) ∈ V | |
2 | df-slot 16490 | . 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴)) | |
3 | 1, 2 | fnmpti 6494 | 1 ⊢ Slot 𝐴 Fn V |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3497 Fn wfn 6353 ‘cfv 6358 Slot cslot 16485 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2796 ax-sep 5206 ax-nul 5213 ax-pr 5333 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-mo 2621 df-eu 2653 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2966 df-ral 3146 df-rex 3147 df-rab 3150 df-v 3499 df-sbc 3776 df-dif 3942 df-un 3944 df-in 3946 df-ss 3955 df-nul 4295 df-if 4471 df-sn 4571 df-pr 4573 df-op 4577 df-uni 4842 df-br 5070 df-opab 5132 df-mpt 5150 df-id 5463 df-xp 5564 df-rel 5565 df-cnv 5566 df-co 5567 df-dm 5568 df-iota 6317 df-fun 6360 df-fn 6361 df-fv 6366 df-slot 16490 |
This theorem is referenced by: (None) |
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