Theorem mndomgmid 39071

Description: Obsolete theorem, use mndmgm 18980 and/or mndid 18983 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 39070	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma)
2		mndoisexid 39069	. 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ ExId )
3	1, 2	elind 4100	1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId ))

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2147   ∩ cin 4092   ExId cexid 39044  Magmacmagm 39048  MndOpcmndo 39066

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-in 4094  df-sgrOLD 39061  df-mndo 39067

This theorem is used by:  ismndo2  39074  rngoidmlem  39136  isdrngo2  39158