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Theorem smgrpismgm 21015
 Description: A semi-group is a magma. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.)
Assertion
Ref Expression
smgrpismgm

Proof of Theorem smgrpismgm
StepHypRef Expression
1 elin 3371 . . 3
21simplbi 446 . 2
3 df-sgr 21014 . 2
42, 3eleq2s 2388 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1696   cin 3164  cass 20995  cmagm 21001  csem 21013 This theorem is referenced by:  mndoismgm  21024  reacomsmgrp2  25447  reacomsmgrp3  25448  resgcom  25454  fprodadd  25455  seqzp2  25458 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
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