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Theorem bj-smgrpssmgmel 37248
Description: Semigroups are magmas (elemental version). (Contributed by BJ, 12-Apr-2024.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-smgrpssmgmel (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

Proof of Theorem bj-smgrpssmgmel
StepHypRef Expression
1 bj-smgrpssmgm 37247 . 2 Smgrp ⊆ Mgm
21sseli 3978 1 (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108  Mgmcmgm 18647  Smgrpcsgrp 18727
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-ss 3967  df-sgrp 18728
This theorem is referenced by: (None)
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