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Theorem mndoismgmOLD 33640
 Description: Obsolete version of mndmgm 17281 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 33638 . 2 (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2 smgrpismgmOLD 33632 . 2 (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
31, 2syl 17 1 (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1988  Magmacmagm 33618  SemiGrpcsem 33630  MndOpcmndo 33636 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-v 3197  df-in 3574  df-sgrOLD 33631  df-mndo 33637 This theorem is referenced by:  mndomgmid  33641  rngo1cl  33709  isdrngo2  33728
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