Theorem bj-ablsscmnel 35377

Description: Abelian groups are commutative monoids (elemental version). This is a shorter proof of ablcmn 19308. (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 35376	. 2 ⊢ Abel ⊆ CMnd
2	1	sseli 3913	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

Syntax hints:   → wi 4   ∈ wcel 2108  CMndccmn 19301  Abelcabl 19302

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-in 3890  df-ss 3900  df-abl 19304

This theorem is referenced by: (None)