Theorem mndoismgmOLD 38549

Description: Obsolete version of mndmgm 18805 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

Step	Hyp	Ref	Expression
1		mndoissmgrpOLD 38547	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2		smgrpismgmOLD 38541	. 2 ⊢ (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
3	1, 2	syl 18	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2142  Magmacmagm 38527  SemiGrpcsem 38539  MndOpcmndo 38545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-in 3911  df-sgrOLD 38540  df-mndo 38546

This theorem is used by:  mndomgmid  38550  rngo1cl  38618  isdrngo2  38637