Theorem bj-ablsscmnel 37222

Description: Abelian groups are commutative monoids (elemental version). This is a shorter proof of ablcmn 19805. (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 37221	. 2 ⊢ Abel ⊆ CMnd
2	1	sseli 3991	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

Syntax hints:   → wi 4   ∈ wcel 2104  CMndccmn 19798  Abelcabl 19799

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1538  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-rab 3433  df-v 3479  df-in 3970  df-ss 3980  df-abl 19801

This theorem is referenced by: (None)