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Theorem mndoismgmOLD 37251
Description: Obsolete version of mndmgm 18674 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 37249 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2 smgrpismgmOLD 37243 . 2 (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
31, 2syl 17 1 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  Magmacmagm 37229  SemiGrpcsem 37241  MndOpcmndo 37247
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-in 3950  df-sgrOLD 37242  df-mndo 37248
This theorem is referenced by:  mndomgmid  37252  rngo1cl  37320  isdrngo2  37339
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