Theorem bj-cmnssmndel 37254

Description: Commutative monoids are monoids (elemental version). This is a more direct proof of cmnmnd 19711, which relies on iscmn 19703. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-cmnssmndel	⊢ (𝐴 ∈ CMnd → 𝐴 ∈ Mnd)

Proof of Theorem bj-cmnssmndel

Step	Hyp	Ref	Expression
1		bj-cmnssmnd 37253	. 2 ⊢ CMnd ⊆ Mnd
2	1	sseli 3939	1 ⊢ (𝐴 ∈ CMnd → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2109  Mndcmnd 18643  CMndccmn 19694

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-rab 3403  df-ss 3928  df-cmn 19696

This theorem is referenced by: (None)