Theorem bj-smgrpssmgmel 36088

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 36087	. 2 ⊢ Smgrp ⊆ Mgm
2	1	sseli 3977	1 ⊢ (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

Syntax hints:   → wi 4   ∈ wcel 2107  Mgmcmgm 18555  Smgrpcsgrp 18605

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-in 3954  df-ss 3964  df-sgrp 18606

This theorem is referenced by: (None)