Theorem bj-smgrpssmgmel 37630

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 37629	. 2 ⊢ Smgrp ⊆ Mgm
2	1	sseli 3918	1 ⊢ (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

Syntax hints:   → wi 4   ∈ wcel 2119  Mgmcmgm 18604  Smgrpcsgrp 18684

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-rab 3393  df-ss 3907  df-sgrp 18685

This theorem is referenced by: (None)