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Mirrors > Home > MPE Home > Th. List > termofn | Structured version Visualization version GIF version |
Description: TermO is a function on Cat. (Contributed by Zhi Wang, 29-Aug-2024.) |
Ref | Expression |
---|---|
termofn | ⊢ TermO Fn Cat |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvex 6895 | . . 3 ⊢ (Base‘𝑐) ∈ V | |
2 | 1 | rabex 5323 | . 2 ⊢ {𝑎 ∈ (Base‘𝑐) ∣ ∀𝑏 ∈ (Base‘𝑐)∃!ℎ ℎ ∈ (𝑏(Hom ‘𝑐)𝑎)} ∈ V |
3 | df-termo 17939 | . 2 ⊢ TermO = (𝑐 ∈ Cat ↦ {𝑎 ∈ (Base‘𝑐) ∣ ∀𝑏 ∈ (Base‘𝑐)∃!ℎ ℎ ∈ (𝑏(Hom ‘𝑐)𝑎)}) | |
4 | 2, 3 | fnmpti 6684 | 1 ⊢ TermO Fn Cat |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2098 ∃!weu 2554 ∀wral 3053 {crab 3424 Fn wfn 6529 ‘cfv 6534 (class class class)co 7402 Basecbs 17145 Hom chom 17209 Catccat 17609 TermOctermo 17936 |
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 5290 ax-nul 5297 ax-pr 5418 |
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 3944 df-un 3946 df-in 3948 df-ss 3958 df-nul 4316 df-if 4522 df-sn 4622 df-pr 4624 df-op 4628 df-uni 4901 df-br 5140 df-opab 5202 df-mpt 5223 df-id 5565 df-xp 5673 df-rel 5674 df-cnv 5675 df-co 5676 df-dm 5677 df-iota 6486 df-fun 6536 df-fn 6537 df-fv 6542 df-termo 17939 |
This theorem is referenced by: dfinito3 17959 |
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