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Theorem zeroofn 17985
Description: ZeroO is a function on Cat. (Contributed by Zhi Wang, 29-Aug-2024.)
Assertion
Ref Expression
zeroofn ZeroO Fn Cat

Proof of Theorem zeroofn
Dummy variable 𝑐 is distinct from all other variables.
StepHypRef Expression
1 fvex 6915 . . 3 (InitO‘𝑐) ∈ V
21inex1 5321 . 2 ((InitO‘𝑐) ∩ (TermO‘𝑐)) ∈ V
3 df-zeroo 17982 . 2 ZeroO = (𝑐 ∈ Cat ↦ ((InitO‘𝑐) ∩ (TermO‘𝑐)))
42, 3fnmpti 6703 1 ZeroO Fn Cat
Colors of variables: wff setvar class
Syntax hints:  cin 3948   Fn wfn 6548  cfv 6553  Catccat 17651  InitOcinito 17977  TermOctermo 17978  ZeroOczeroo 17979
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 2166  ax-ext 2699  ax-sep 5303  ax-nul 5310  ax-pr 5433
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2529  df-eu 2558  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ne 2938  df-ral 3059  df-rex 3068  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4913  df-br 5153  df-opab 5215  df-mpt 5236  df-id 5580  df-xp 5688  df-rel 5689  df-cnv 5690  df-co 5691  df-dm 5692  df-iota 6505  df-fun 6555  df-fn 6556  df-fv 6561  df-zeroo 17982
This theorem is referenced by: (None)
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