Theorem mndoismgmOLD 37857

Description: Obsolete version of mndmgm 18767 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 37855	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2		smgrpismgmOLD 37849	. 2 ⊢ (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
3	1, 2	syl 17	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma)

Syntax hints:   → wi 4   ∈ wcel 2106  Magmacmagm 37835  SemiGrpcsem 37847  MndOpcmndo 37853

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-in 3970  df-sgrOLD 37848  df-mndo 37854

This theorem is referenced by:  mndomgmid  37858  rngo1cl  37926  isdrngo2  37945