Theorem thincssc 48693

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 48691	. 2 ⊢ (𝑐 ∈ ThinCat → 𝑐 ∈ Cat)
2	1	ssriv 4012	1 ⊢ ThinCat ⊆ Cat

Syntax hints:   ⊆ wss 3976  Catccat 17722  ThinCatcthinc 48686

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-nul 5324

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-mo 2543  df-clab 2718  df-cleq 2732  df-clel 2819  df-ne 2947  df-ral 3068  df-rex 3077  df-rab 3444  df-v 3490  df-sbc 3805  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-iota 6525  df-fv 6581  df-ov 7451  df-thinc 48687

This theorem is referenced by: (None)