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Theorem mndoisexid 21920
 Description: A monoid has an identity element. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.)
Assertion
Ref Expression
mndoisexid MndOp

Proof of Theorem mndoisexid
StepHypRef Expression
1 elin 3522 . . 3
21simprbi 451 . 2
3 df-mndo 21918 . 2 MndOp
42, 3eleq2s 2527 1 MndOp
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725   cin 3311   cexid 21894  csem 21910  MndOpcmndo 21917 This theorem is referenced by:  mndomgmid  21922  rngo1cl  22009 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-mndo 21918
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