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Theorem bj-grpssmndel 35090
Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18229. (Contributed by BJ, 5-Jan-2024.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-grpssmndel (𝐴 ∈ Grp → 𝐴 ∈ Mnd)

Proof of Theorem bj-grpssmndel
StepHypRef Expression
1 bj-grpssmnd 35089 . 2 Grp ⊆ Mnd
21sseli 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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