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Theorem zeroofn 17948
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 6897 . . 3 (InitO‘𝑐) ∈ V
21inex1 5310 . 2 ((InitO‘𝑐) ∩ (TermO‘𝑐)) ∈ V
3 df-zeroo 17945 . 2 ZeroO = (𝑐 ∈ Cat ↦ ((InitO‘𝑐) ∩ (TermO‘𝑐)))
42, 3fnmpti 6686 1 ZeroO Fn Cat
Colors of variables: wff setvar class
Syntax hints:  cin 3942   Fn wfn 6531  cfv 6536  Catccat 17614  InitOcinito 17940  TermOctermo 17941  ZeroOczeroo 17942
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 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420
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 2528  df-eu 2557  df-clab 2704  df-cleq 2718  df-clel 2804  df-nfc 2879  df-ne 2935  df-ral 3056  df-rex 3065  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-opab 5204  df-mpt 5225  df-id 5567  df-xp 5675  df-rel 5676  df-cnv 5677  df-co 5678  df-dm 5679  df-iota 6488  df-fun 6538  df-fn 6539  df-fv 6544  df-zeroo 17945
This theorem is referenced by: (None)
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