Theorem mndoismgmOLD 33669

Description: Obsolete version of mndmgm 17300 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 e. MndOp -> G e. Magma )

Proof of Theorem mndoismgmOLD

Step	Hyp	Ref	Expression
1		mndoissmgrpOLD 33667	. 2 |- ( G e. MndOp -> G e. SemiGrp )
2		smgrpismgmOLD 33661	. 2 |- ( G e. SemiGrp -> G e. Magma )
3	1, 2	syl 17	1 |- ( G e. MndOp -> G e. Magma )

Syntax hints:   -> wi 4   e. wcel 1990   Magmacmagm 33647   SemiGrpcsem 33659  MndOpcmndo 33665

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-in 3581  df-sgrOLD 33660  df-mndo 33666

This theorem is referenced by:  mndomgmid  33670  rngo1cl  33738  isdrngo2  33757