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Theorem mndoismgm 25047
Description: A monoid is a magma. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.)
Assertion
Ref Expression
mndoismgm  |-  ( G  e. MndOp  ->  G  e.  Magma )

Proof of Theorem mndoismgm
StepHypRef Expression
1 mndoissmgrp 25045 . 2  |-  ( G  e. MndOp  ->  G  e.  SemiGrp )
2 smgrpismgm 25038 . 2  |-  ( G  e.  SemiGrp  ->  G  e.  Magma )
31, 2syl 16 1  |-  ( G  e. MndOp  ->  G  e.  Magma )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1767   Magmacmagm 25024   SemiGrpcsem 25036  MndOpcmndo 25043
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-in 3483  df-sgr 25037  df-mndo 25044
This theorem is referenced by:  mndomgmid  25048  rngo1cl  25135  isdrngo2  29992
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