Theorem termofn 17890

Description: TermO is a function on Cat. (Contributed by Zhi Wang, 29-Aug-2024.)

Assertion

Ref	Expression
termofn	⊢ TermO Fn Cat

Proof of Theorem termofn

Dummy variables 𝑎 𝑏 𝑐 ℎ are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		fvex 6830	. . 3 ⊢ (Base‘𝑐) ∈ V
2	1	rabex 5272	. 2 ⊢ {𝑎 ∈ (Base‘𝑐) ∣ ∀𝑏 ∈ (Base‘𝑐)∃!ℎ ℎ ∈ (𝑏(Hom ‘𝑐)𝑎)} ∈ V
3		df-termo 17887	. 2 ⊢ TermO = (𝑐 ∈ Cat ↦ {𝑎 ∈ (Base‘𝑐) ∣ ∀𝑏 ∈ (Base‘𝑐)∃!ℎ ℎ ∈ (𝑏(Hom ‘𝑐)𝑎)})
4	2, 3	fnmpti 6619	1 ⊢ TermO Fn Cat

Syntax hints:   ∈ wcel 2111  ∃!weu 2563  ∀wral 3047  {crab 3395   Fn wfn 6471  ‘cfv 6476  (class class class)co 7341  Basecbs 17115  Hom chom 17167  Catccat 17565  TermOctermo 17884

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-10 2144  ax-11 2160  ax-12 2180  ax-ext 2703  ax-sep 5229  ax-nul 5239  ax-pr 5365

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-mo 2535  df-eu 2564  df-clab 2710  df-cleq 2723  df-clel 2806  df-nfc 2881  df-ne 2929  df-ral 3048  df-rex 3057  df-rab 3396  df-v 3438  df-dif 3900  df-un 3902  df-in 3904  df-ss 3914  df-nul 4279  df-if 4471  df-pw 4547  df-sn 4572  df-pr 4574  df-op 4578  df-uni 4855  df-br 5087  df-opab 5149  df-mpt 5168  df-id 5506  df-xp 5617  df-rel 5618  df-cnv 5619  df-co 5620  df-dm 5621  df-iota 6432  df-fun 6478  df-fn 6479  df-fv 6484  df-termo 17887

This theorem is referenced by:  dfinito3  17907  termopropdlem  49273  termopropd  49276