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Theorem mndomgmid 37878
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 37877 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
2 mndoisexid 37876 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ ExId )
31, 2elind 4200 1 (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108  cin 3950   ExId cexid 37851  Magmacmagm 37855  MndOpcmndo 37873
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-in 3958  df-sgrOLD 37868  df-mndo 37874
This theorem is referenced by:  ismndo2  37881  rngoidmlem  37943  isdrngo2  37965
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