Theorem bj-mndsssmgrpel 36755

Description: Monoids are semigroups (elemental version). (Contributed by BJ, 11-Apr-2024.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-mndsssmgrpel	⊢ (𝐺 ∈ Mnd → 𝐺 ∈ Smgrp)

Proof of Theorem bj-mndsssmgrpel

Step	Hyp	Ref	Expression
1		bj-mndsssmgrp 36754	. 2 ⊢ Mnd ⊆ Smgrp
2	1	sseli 3976	1 ⊢ (𝐺 ∈ Mnd → 𝐺 ∈ Smgrp)

Syntax hints:   → wi 4   ∈ wcel 2098  Smgrpcsgrp 18683  Mndcmnd 18699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3429  df-v 3473  df-in 3954  df-ss 3964  df-mnd 18700

This theorem is referenced by: (None)