Theorem mndoisexid 38621

Description: Obsolete theorem, use mndid 18850 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 4151	. 2 ⊢ (𝐺 ∈ (SemiGrp ∩ ExId ) → 𝐺 ∈ ExId )
2		df-mndo 38619	. 2 ⊢ MndOp = (SemiGrp ∩ ExId )
3	1, 2	eleq2s 2880	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ ExId )

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145   ∩ cin 3901   ExId cexid 38596  SemiGrpcsem 38612  MndOpcmndo 38618

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 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-in 3909  df-mndo 38619

This theorem is used by:  mndomgmid  38623  rngo1cl  38691