Theorem mndoisexid 38879

Description: Obsolete theorem, use mndid 18934 instead. A monoid has an identity element. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
mndoisexid	⊢ (𝐺 ∈ MndOp → 𝐺 ∈ ExId )

Proof of Theorem mndoisexid

Step	Hyp	Ref	Expression
1		elinel2 4099	. 2 ⊢ (𝐺 ∈ (SemiGrp ∩ ExId ) → 𝐺 ∈ ExId )
2		df-mndo 38877	. 2 ⊢ MndOp = (SemiGrp ∩ ExId )
3	1, 2	eleq2s 2878	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ ExId )

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2144   ∩ cin 4089   ExId cexid 38854  SemiGrpcsem 38870  MndOpcmndo 38876

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-in 4091  df-mndo 38877

This theorem is used by:  mndomgmid  38881  rngo1cl  38949