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Theorem bj-smgrpssmgmel 36455
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 36454 . 2 Smgrp ⊆ Mgm
21sseli 3979 1 (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2104  Mgmcmgm 18565  Smgrpcsgrp 18645
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 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1542  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-rab 3431  df-v 3474  df-in 3956  df-ss 3966  df-sgrp 18646
This theorem is referenced by: (None)
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