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Theorem thinccd 49073
Description: A thin category is a category (deduction form). (Contributed by Zhi Wang, 24-Sep-2024.)
Hypothesis
Ref Expression
thinccd.c (𝜑𝐶 ∈ ThinCat)
Assertion
Ref Expression
thinccd (𝜑𝐶 ∈ Cat)

Proof of Theorem thinccd
StepHypRef Expression
1 thinccd.c . 2 (𝜑𝐶 ∈ ThinCat)
2 thincc 49072 . 2 (𝐶 ∈ ThinCat → 𝐶 ∈ Cat)
31, 2syl 17 1 (𝜑𝐶 ∈ Cat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108  Catccat 17707  ThinCatcthinc 49067
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 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-nul 5306
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-mo 2540  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-sbc 3789  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569  df-ov 7434  df-thinc 49068
This theorem is referenced by:  thincid  49081  thincmon  49082  thincepi  49083  oppcthinco  49088  functhinclem4  49096  functhinc  49097  thincciso  49102  thinccisod  49103  thincsect  49114  thincinv  49116  thinciso  49117  thinccic  49118  termccd  49126
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