Theorem bj-ablsscmnel 37951

Description: Abelian groups are commutative monoids (elemental version). This is a shorter proof of ablcmn 19863. (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 37950	. 2 ⊢ Abel ⊆ CMnd
2	1	sseli 3932	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2142  CMndccmn 19856  Abelcabl 19857

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3416  df-v 3456  df-in 3911  df-ss 3921  df-abl 19859

This theorem is used by: (None)