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Theorem mndoisass 25356
Description: A monoid is associative. (Contributed by FL, 2-Nov-2009.)
Assertion
Ref Expression
mndoisass  |-  ( G  e. MndOp  ->  G  e.  Ass )

Proof of Theorem mndoisass
StepHypRef Expression
1 mndoissmgrp 21006 . 2  |-  ( G  e. MndOp  ->  G  e.  SemiGrp )
2 smgrpisass 21000 . 2  |-  ( G  e.  SemiGrp  ->  G  e.  Ass )
31, 2syl 15 1  |-  ( G  e. MndOp  ->  G  e.  Ass )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   Asscass 20979   SemiGrpcsem 20997  MndOpcmndo 21004
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-sgr 20998  df-mndo 21005
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