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Theorem bj-cmnssmndel 36620
Description: Commutative monoids are monoids (elemental version). This is a more direct proof of cmnmnd 19713, which relies on iscmn 19705. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-cmnssmndel (𝐴 ∈ CMnd → 𝐴 ∈ Mnd)

Proof of Theorem bj-cmnssmndel
StepHypRef Expression
1 bj-cmnssmnd 36619 . 2 CMnd ⊆ Mnd
21sseli 3978 1 (𝐴 ∈ CMnd → 𝐴 ∈ Mnd)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  Mndcmnd 18665  CMndccmn 19696
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-v 3475  df-in 3955  df-ss 3965  df-cmn 19698
This theorem is referenced by: (None)
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