Theorem fnmgp

Description: The multiplicative group operator is a function. (Contributed by Mario Carneiro, 11-Mar-2015)

	Ref	Expression
Assertion	fnmgp	$$⊢\mathrm{mulGrp}Fn\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ovex	$$⊢x\mathrm{sSet}⟨{+}_{\mathrm{ndx}},{\cdot }_x⟩\in \mathrm{V}$$
2		df-mgp	$$⊢\mathrm{mulGrp}=\left(x\in \mathrm{V}⟼x\mathrm{sSet}⟨{+}_{\mathrm{ndx}},{\cdot }_x⟩\right)$$
3	1 2	fnmpti	$$⊢\mathrm{mulGrp}Fn\mathrm{V}$$