Theorem thincssc 47646

Description: A thin category is a category. (Contributed by Zhi Wang, 17-Sep-2024.)

Assertion

Ref	Expression
thincssc	⊢ ThinCat ⊆ Cat

Proof of Theorem thincssc

Step	Hyp	Ref	Expression
1		thincc 47644	. 2 ⊢ (𝑐 ∈ ThinCat → 𝑐 ∈ Cat)
2	1	ssriv 3987	1 ⊢ ThinCat ⊆ Cat

Syntax hints:   ⊆ wss 3949  Catccat 17608  ThinCatcthinc 47639

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-nul 5307

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-mo 2535  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2942  df-ral 3063  df-rex 3072  df-rab 3434  df-v 3477  df-sbc 3779  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4910  df-br 5150  df-iota 6496  df-fv 6552  df-ov 7412  df-thinc 47640

This theorem is referenced by: (None)