Theorem mndomgmid 38555

Description: Obsolete theorem, use mndmgm 18821 and/or mndid 18824 instead. A monoid is a magma with an identity element. (Contributed by FL, 18-Feb-2010.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
mndomgmid	⊢ (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))

Proof of Theorem mndomgmid

Step	Hyp	Ref	Expression
1		mndoismgmOLD 38554	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
2		mndoisexid 38553	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ ExId )
3	1, 2	elind 4153	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2146   ∩ cin 3905   ExId cexid 38528  Magmacmagm 38532  MndOpcmndo 38550

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 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-in 3913  df-sgrOLD 38545  df-mndo 38551

This theorem is used by:  ismndo2  38558  rngoidmlem  38620  isdrngo2  38642