Theorem bj-smgrpssmgmel 38284

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 38283	. 2 ⊢ Smgrp ⊆ Mgm
2	1	sseli 3904	1 ⊢ (𝐺 ∈ Smgrp → 𝐺 ∈ Mgm)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2144  Mgmcmgm 18820  Smgrpcsgrp 18913

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-ss 3896  df-sgrp 18914

This theorem is used by: (None)