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Theorem mndoisass 25459
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 21022 . 2  |-  ( G  e. MndOp  ->  G  e.  SemiGrp )
2 smgrpisass 21016 . 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 1696   Asscass 20995   SemiGrpcsem 21013  MndOpcmndo 21020
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-sgr 21014  df-mndo 21021
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