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Theorem mndoismgmOLD 36036
Description: Obsolete version of mndmgm 18402 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 36034 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2 smgrpismgmOLD 36028 . 2 (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
31, 2syl 17 1 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Magmacmagm 36014  SemiGrpcsem 36026  MndOpcmndo 36032
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3431  df-in 3893  df-sgrOLD 36027  df-mndo 36033
This theorem is referenced by:  mndomgmid  36037  rngo1cl  36105  isdrngo2  36124
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