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Theorem bj-smgrpssmgmel 37212
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 37211 . 2 Smgrp ⊆ Mgm
21sseli 3991 1 (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2104  Mgmcmgm 18652  Smgrpcsgrp 18732
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-rab 3433  df-ss 3980  df-sgrp 18733
This theorem is referenced by: (None)
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