Theorem bj-ablsscmnel 37867

Description: Abelian groups are commutative monoids (elemental version). This is a shorter proof of ablcmn 19856. (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 37866	. 2 ⊢ Abel ⊆ CMnd
2	1	sseli 3932	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

Syntax hints:   → wi 4   ∈ wcel 2141  CMndccmn 19849  Abelcabl 19850

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3415  df-v 3455  df-in 3911  df-ss 3921  df-abl 19852

This theorem is referenced by: (None)