Theorem bj-cmnssmndel 37603

Description: Commutative monoids are monoids (elemental version). This is a more direct proof of cmnmnd 19763, which relies on iscmn 19755. (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 37602	. 2 ⊢ CMnd ⊆ Mnd
2	1	sseli 3918	1 ⊢ (𝐴 ∈ CMnd → 𝐴 ∈ Mnd)

Syntax hints:   → wi 4   ∈ wcel 2114  Mndcmnd 18693  CMndccmn 19746

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-ss 3907  df-cmn 19748

This theorem is referenced by: (None)