Theorem bj-smgrpssmgmel 35440

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 35439	. 2 ⊢ Smgrp ⊆ Mgm
2	1	sseli 3917	1 ⊢ (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

Syntax hints:   → wi 4   ∈ wcel 2106  Mgmcmgm 18324  Smgrpcsgrp 18374

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-in 3894  df-ss 3904  df-sgrp 18375

This theorem is referenced by: (None)