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Theorem bj-grpssmndel 35446
Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18584. (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 35445 . 2 Grp ⊆ Mnd
21sseli 3917 1 (𝐴 ∈ Grp → 𝐴 ∈ Mnd)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Mndcmnd 18385  Grpcgrp 18577
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-in 3894  df-ss 3904  df-grp 18580
This theorem is referenced by: (None)
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