Theorem bj-smgrpssmgmel 37946

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 37945	. 2 ⊢ Smgrp ⊆ Mgm
2	1	sseli 3936	1 ⊢ (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2146  Mgmcmgm 18721  Smgrpcsgrp 18801

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 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-rab 3420  df-ss 3925  df-sgrp 18802

This theorem is used by: (None)