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Theorem mndoismgmOLD 36379
Description: Obsolete version of mndmgm 18571 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 36377 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2 smgrpismgmOLD 36371 . 2 (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
31, 2syl 17 1 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Magmacmagm 36357  SemiGrpcsem 36369  MndOpcmndo 36375
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3449  df-in 3921  df-sgrOLD 36370  df-mndo 36376
This theorem is referenced by:  mndomgmid  36380  rngo1cl  36448  isdrngo2  36467
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