Theorem bj-smgrpssmgmel 38395

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 38394	. 2 ⊢ Smgrp ⊆ Mgm
2	1	sseli 3909	1 ⊢ (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2147  Mgmcmgm 18846  Smgrpcsgrp 18939

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-ss 3901  df-sgrp 18940

This theorem is used by: (None)