Theorem mndlid

Description: The identity element of a monoid is a left identity. (Contributed by NM, 18-Aug-2011)

	Ref	Expression
Hypotheses	mndlrid.b	|- B = ( Base ` G )
	mndlrid.p	|- .+ = ( +g ` G )
	mndlrid.o	|- .0. = ( 0g ` G )
Assertion	mndlid	|- ( ( G e. Mnd /\ X e. B ) -> ( .0. .+ X ) = X )

Proof

Step	Hyp	Ref	Expression
1		mndlrid.b	|- B = ( Base ` G )
2		mndlrid.p	|- .+ = ( +g ` G )
3		mndlrid.o	|- .0. = ( 0g ` G )
4	1 2 3	mndlrid	|- ( ( G e. Mnd /\ X e. B ) -> ( ( .0. .+ X ) = X /\ ( X .+ .0. ) = X ) )
5	4	simpld	|- ( ( G e. Mnd /\ X e. B ) -> ( .0. .+ X ) = X )