Theorem bj-cmnssmndel 36805

Description: Commutative monoids are monoids (elemental version). This is a more direct proof of cmnmnd 19751, which relies on iscmn 19743. (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 36804	. 2 ⊢ CMnd ⊆ Mnd
2	1	sseli 3969	1 ⊢ (𝐴 ∈ CMnd → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2098  Mndcmnd 18688  CMndccmn 19734

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rab 3420  df-ss 3958  df-cmn 19736

This theorem is referenced by: (None)