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Theorem mndoismgm 21921
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 21919 . 2  |-  ( G  e. MndOp  ->  G  e.  SemiGrp )
2 smgrpismgm 21912 . 2  |-  ( G  e.  SemiGrp  ->  G  e.  Magma )
31, 2syl 16 1  |-  ( G  e. MndOp  ->  G  e.  Magma )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   Magmacmagm 21898   SemiGrpcsem 21910  MndOpcmndo 21917
This theorem is referenced by:  mndomgmid  21922  rngo1cl  22009  isdrngo2  26565
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-sgr 21911  df-mndo 21918
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