Theorem bj-grpssmndel 35373

Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18499. (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 35372	. 2 ⊢ Grp ⊆ Mnd
2	1	sseli 3913	1 ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2108  Mndcmnd 18300  Grpcgrp 18492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-in 3890  df-ss 3900  df-grp 18495

This theorem is referenced by: (None)