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Theorem mndoissmgrpOLD 26115
Description: Obsolete version of mndsgrp 16591 as of 3-Feb-2020. A monoid is a semi-group. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
mndoissmgrpOLD  |-  ( G  e. MndOp  ->  G  e.  SemiGrp )

Proof of Theorem mndoissmgrpOLD
StepHypRef Expression
1 elin 3628 . . 3  |-  ( G  e.  ( SemiGrp  i^i  ExId  )  <-> 
( G  e.  SemiGrp  /\  G  e.  ExId  ) )
21simplbi 466 . 2  |-  ( G  e.  ( SemiGrp  i^i  ExId  )  ->  G  e.  SemiGrp )
3 df-mndo 26114 . 2  |- MndOp  =  (
SemiGrp  i^i  ExId  )
42, 3eleq2s 2557 1  |-  ( G  e. MndOp  ->  G  e.  SemiGrp )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1897    i^i cin 3414    ExId cexid 26090   SemiGrpcsem 26106  MndOpcmndo 26113
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-11 1930  ax-12 1943  ax-13 2101  ax-ext 2441
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2591  df-v 3058  df-in 3422  df-mndo 26114
This theorem is referenced by:  mndoismgmOLD  26117
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