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Theorem mndomgmid 33302
Description: A monoid is a magma with an identity element. (Contributed by FL, 18-Feb-2010.) (New usage is discouraged.)
Assertion
Ref Expression
mndomgmid (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))

Proof of Theorem mndomgmid
StepHypRef Expression
1 mndoismgmOLD 33301 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
2 mndoisexid 33300 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ ExId )
31, 2elind 3776 1 (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1987  cin 3554   ExId cexid 33275  Magmacmagm 33279  MndOpcmndo 33297
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-in 3562  df-sgrOLD 33292  df-mndo 33298
This theorem is referenced by:  ismndo2  33305  rngoidmlem  33367  isdrngo2  33389
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