Theorem thincssc 49921

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 49919	. 2 ⊢ (𝑐 ∈ ThinCat → 𝑐 ∈ Cat)
2	1	ssriv 3926	1 ⊢ ThinCat ⊆ Cat

Syntax hints:   ⊆ wss 3890  Catccat 17628  ThinCatcthinc 49914

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-nul 5235

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-mo 2543  df-clab 2719  df-cleq 2732  df-clel 2815  df-ne 2936  df-ral 3055  df-rex 3065  df-rab 3393  df-v 3434  df-sbc 3731  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4269  df-if 4462  df-sn 4563  df-pr 4565  df-op 4569  df-uni 4846  df-br 5080  df-iota 6448  df-fv 6500  df-ov 7366  df-thinc 49915

This theorem is referenced by: (None)