Theorem thincssc 49777

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 49775	. 2 ⊢ (𝑐 ∈ ThinCat → 𝑐 ∈ Cat)
2	1	ssriv 3939	1 ⊢ ThinCat ⊆ Cat

Syntax hints:   ⊆ wss 3903  Catccat 17599  ThinCatcthinc 49770

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-nul 5253

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-mo 2540  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-ral 3053  df-rex 3063  df-rab 3402  df-v 3444  df-sbc 3743  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-uni 4866  df-br 5101  df-iota 6456  df-fv 6508  df-ov 7371  df-thinc 49771

This theorem is referenced by: (None)