Theorem bj-mndsssmgrpel 37716

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 37715	. 2 ⊢ Mnd ⊆ Smgrp
2	1	sseli 3932	1 ⊢ (𝐺 ∈ Mnd → 𝐺 ∈ Smgrp)

Syntax hints:   → wi 4   ∈ wcel 2141  Smgrpcsgrp 18733  Mndcmnd 18749

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-ss 3921  df-mnd 18750

This theorem is referenced by: (None)