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Theorem mndomgmid 25006
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 mndoismgm 25005 . 2  |-  ( G  e. MndOp  ->  G  e.  Magma )
2 mndoisexid 25004 . 2  |-  ( G  e. MndOp  ->  G  e.  ExId  )
31, 2elind 3681 1  |-  ( G  e. MndOp  ->  G  e.  (
Magma  i^i  ExId  ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1762    i^i cin 3468    ExId cexid 24978   Magmacmagm 24982  MndOpcmndo 25001
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-v 3108  df-in 3476  df-sgr 24995  df-mndo 25002
This theorem is referenced by:  ismndo2  25009  rngoidmlem  25087  isdrngo2  29951
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