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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 18825. (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 36150 | . 2 ⊢ Grp ⊆ Mnd | |
2 | 1 | sseli 3978 | 1 ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2106 Mndcmnd 18624 Grpcgrp 18818 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-rab 3433 df-v 3476 df-in 3955 df-ss 3965 df-grp 18821 |
This theorem is referenced by: (None) |
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