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Theorem bj-grpssmndel 36151
Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18825. (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 36150 . 2 Grp ⊆ Mnd
21sseli 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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