Theorem bj-grpssmndel 36460

Description: Groups are monoids (elemental version). Shorter proof of grpmnd 18863. (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 36459	. 2 ⊢ Grp ⊆ Mnd
2	1	sseli 3979	1 ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2105  Mndcmnd 18660  Grpcgrp 18856

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 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-v 3475  df-in 3956  df-ss 3966  df-grp 18859

This theorem is referenced by: (None)