Theorem bj-cmnssmndel 36675

Description: Commutative monoids are monoids (elemental version). This is a more direct proof of cmnmnd 19736, which relies on iscmn 19728. (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 36674	. 2 ⊢ CMnd ⊆ Mnd
2	1	sseli 3974	1 ⊢ (𝐴 ∈ CMnd → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2099  Mndcmnd 18679  CMndccmn 19719

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 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3428  df-v 3471  df-in 3951  df-ss 3961  df-cmn 19721

This theorem is referenced by: (None)