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Theorem mndomgmid 25771
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  e. MndOp  ->  G  e.  (
Magma  i^i  ExId  ) )

Proof of Theorem mndomgmid
StepHypRef Expression
1 mndoismgmOLD 25770 . 2  |-  ( G  e. MndOp  ->  G  e.  Magma )
2 mndoisexid 25769 . 2  |-  ( G  e. MndOp  ->  G  e.  ExId  )
31, 2elind 3629 1  |-  ( G  e. MndOp  ->  G  e.  (
Magma  i^i  ExId  ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1844    i^i cin 3415    ExId cexid 25743   Magmacmagm 25747  MndOpcmndo 25766
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382
This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-v 3063  df-in 3423  df-sgrOLD 25760  df-mndo 25767
This theorem is referenced by:  ismndo2  25774  rngoidmlem  25852  isdrngo2  31656
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