Theorem bj-smgrpssmgmel 37445

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

Step	Hyp	Ref	Expression
1		bj-smgrpssmgm 37444	. 2 ⊢ Smgrp ⊆ Mgm
2	1	sseli 3930	1 ⊢ (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

Syntax hints:   → wi 4   ∈ wcel 2114  Mgmcmgm 18567  Smgrpcsgrp 18647

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3401  df-ss 3919  df-sgrp 18648

This theorem is referenced by: (None)