Theorem mndplusf

Description: The group addition operation is a function. (Contributed by Mario Carneiro, 14-Aug-2015) (Proof shortened by AV, 3-Feb-2020)

	Ref	Expression
Hypotheses	mndplusf.1	|- B = ( Base ` G )
	mndplusf.2	|- .+^ = ( +f ` G )
Assertion	mndplusf	|- ( G e. Mnd -> .+^ : ( B X. B ) --> B )

Proof

Step	Hyp	Ref	Expression
1		mndplusf.1	|- B = ( Base ` G )
2		mndplusf.2	|- .+^ = ( +f ` G )
3		mndmgm	|- ( G e. Mnd -> G e. Mgm )
4	1 2	mgmplusf	|- ( G e. Mgm -> .+^ : ( B X. B ) --> B )
5	3 4	syl	|- ( G e. Mnd -> .+^ : ( B X. B ) --> B )