Theorem mndoismgmOLD 38996

Description: Obsolete version of mndmgm 18959 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 38994	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2		smgrpismgmOLD 38988	. 2 ⊢ (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
3	1, 2	syl 18	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2147  Magmacmagm 38974  SemiGrpcsem 38986  MndOpcmndo 38992

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-in 4094  df-sgrOLD 38987  df-mndo 38993

This theorem is used by:  mndomgmid  38997  rngo1cl  39065  isdrngo2  39084