Theorem bj-ablsscmnel 37776

Description: Abelian groups are commutative monoids (elemental version). This is a shorter proof of ablcmn 19829. (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 37775	. 2 ⊢ Abel ⊆ CMnd
2	1	sseli 3934	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

Syntax hints:   → wi 4   ∈ wcel 2144  CMndccmn 19822  Abelcabl 19823

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1565  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-rab 3417  df-v 3458  df-in 3913  df-ss 3923  df-abl 19825

This theorem is referenced by: (None)