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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-grpssmndel | Structured version Visualization version GIF version |
Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18229. (Contributed by BJ, 5-Jan-2024.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-grpssmndel | ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-grpssmnd 35089 | . 2 ⊢ Grp ⊆ Mnd | |
2 | 1 | sseli 3874 | 1 ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2114 Mndcmnd 18030 Grpcgrp 18222 |
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 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2711 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2718 df-cleq 2731 df-clel 2812 df-rab 3063 df-v 3401 df-in 3851 df-ss 3861 df-grp 18225 |
This theorem is referenced by: (None) |
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