Theorem mndoismgmOLD 38724

Description: Obsolete version of mndmgm 18892 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 38722	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp)
2		smgrpismgmOLD 38716	. 2 ⊢ (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma)
3	1, 2	syl 18	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145  Magmacmagm 38702  SemiGrpcsem 38714  MndOpcmndo 38720

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-in 3905  df-sgrOLD 38715  df-mndo 38721

This theorem is used by:  mndomgmid  38725  rngo1cl  38793  isdrngo2  38812