Theorem mndoismgmOLD 37474

Description: Obsolete version of mndmgm 18704 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 37472	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2		smgrpismgmOLD 37466	. 2 ⊢ (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
3	1, 2	syl 17	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma)

Syntax hints:   → wi 4   ∈ wcel 2098  Magmacmagm 37452  SemiGrpcsem 37464  MndOpcmndo 37470

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 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-in 3951  df-sgrOLD 37465  df-mndo 37471

This theorem is referenced by:  mndomgmid  37475  rngo1cl  37543  isdrngo2  37562