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| Mirrors > Home > MPE Home > Th. List > Mathboxes > thinccd | Structured version Visualization version GIF version | ||
| Description: A thin category is a category (deduction form). (Contributed by Zhi Wang, 24-Sep-2024.) |
| Ref | Expression |
|---|---|
| thinccd.c | ⊢ (𝜑 → 𝐶 ∈ ThinCat) |
| Ref | Expression |
|---|---|
| thinccd | ⊢ (𝜑 → 𝐶 ∈ Cat) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | thinccd.c | . 2 ⊢ (𝜑 → 𝐶 ∈ ThinCat) | |
| 2 | thincc 49072 | . 2 ⊢ (𝐶 ∈ ThinCat → 𝐶 ∈ Cat) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐶 ∈ 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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