Theorem bj-grpssmndel 34579

Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18103. (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 34578	. 2 ⊢ Grp ⊆ Mnd
2	1	sseli 3956	1 ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2113  Mndcmnd 17904  Grpcgrp 18096

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2792

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2799  df-cleq 2813  df-clel 2892  df-nfc 2962  df-rab 3146  df-in 3936  df-ss 3945  df-grp 18099

This theorem is referenced by: (None)