Theorem bj-ablsscmnel 38392

Description: Abelian groups are commutative monoids (elemental version). This is a shorter proof of ablcmn 20031. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ablsscmnel	⊢ (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

Proof of Theorem bj-ablsscmnel

Step	Hyp	Ref	Expression
1		bj-ablsscmn 38391	. 2 ⊢ Abel ⊆ CMnd
2	1	sseli 3909	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2147  CMndccmn 20024  Abelcabl 20025

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-in 4094  df-abl 20027

This theorem is used by: (None)