Theorem bj-grpssmndel 38027

Description: Groups are monoids (elemental version). Shorter proof of grpmnd 19064. (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 38026	. 2 ⊢ Grp ⊆ Mnd
2	1	sseli 3927	1 ⊢ (𝐴 ∈ Grp → 𝐴 ∈ Mnd)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145  Mndcmnd 18836  Grpcgrp 19057

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-ss 3916  df-grp 19060

This theorem is used by: (None)