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Theorem mndoismgmOLD 34590
 Description: Obsolete version of mndmgm 17762 as of 3-Feb-2020. A monoid is a magma. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
mndoismgmOLD (𝐺 ∈ MndOp → 𝐺 ∈ Magma)

Proof of Theorem mndoismgmOLD
StepHypRef Expression
1 mndoissmgrpOLD 34588 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2 smgrpismgmOLD 34582 . 2 (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
31, 2syl 17 1 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2050  Magmacmagm 34568  SemiGrpcsem 34580  MndOpcmndo 34586 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2744 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2753  df-cleq 2765  df-clel 2840  df-nfc 2912  df-v 3411  df-in 3830  df-sgrOLD 34581  df-mndo 34587 This theorem is referenced by:  mndomgmid  34591  rngo1cl  34659  isdrngo2  34678
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