Theorem bj-grpssmndel 37315

Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18853. (Contributed by BJ, 5-Jan-2024.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-grpssmndel	⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd)

Proof of Theorem bj-grpssmndel

Step	Hyp	Ref	Expression
1		bj-grpssmnd 37314	. 2 ⊢ Grp ⊆ Mnd
2	1	sseli 3930	1 ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2111  Mndcmnd 18642  Grpcgrp 18846

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-ss 3919  df-grp 18849

This theorem is referenced by: (None)