Theorem mgptset

Description: Topology component of the multiplication group. (Contributed by Mario Carneiro, 5-Oct-2015)

	Ref	Expression
Hypothesis	mgpbas.1	$$⊢M={\mathrm{mulGrp}}_R$$
Assertion	mgptset	$$⊢\mathrm{TopSet}\left(R\right)=\mathrm{TopSet}\left(M\right)$$

Proof

Step	Hyp	Ref	Expression
1		mgpbas.1	$$⊢M={\mathrm{mulGrp}}_R$$
2		df-tset	$$⊢\mathrm{TopSet}=\mathrm{Slot}9$$
3		9nn	$$⊢9\in \mathbb{N}$$
4		2re	$$⊢2\in ℝ$$
5		2lt9	$$⊢2<9$$
6	4 5	gtneii	$$⊢9\ne 2$$
7	1 2 3 6	mgplem	$$⊢\mathrm{TopSet}\left(R\right)=\mathrm{TopSet}\left(M\right)$$