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Theorem mndomgmid 37858
Description: A monoid is a magma with an identity element. (Contributed by FL, 18-Feb-2010.) (New usage is discouraged.)
Assertion
Ref Expression
mndomgmid (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))

Proof of Theorem mndomgmid
StepHypRef Expression
1 mndoismgmOLD 37857 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
2 mndoisexid 37856 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ ExId )
31, 2elind 4210 1 (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  cin 3962   ExId cexid 37831  Magmacmagm 37835  MndOpcmndo 37853
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-in 3970  df-sgrOLD 37848  df-mndo 37854
This theorem is referenced by:  ismndo2  37861  rngoidmlem  37923  isdrngo2  37945
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