Theorem oppgtset

Description: Topology of an opposite group. (Contributed by Mario Carneiro, 17-Sep-2015)

	Ref	Expression
Hypotheses	oppgbas.1	⊢ 𝑂 = ( oppg ‘ 𝑅 )
	oppgtset.2	⊢ 𝐽 = ( TopSet ‘ 𝑅 )
Assertion	oppgtset	⊢ 𝐽 = ( TopSet ‘ 𝑂 )

Proof

Step	Hyp	Ref	Expression
1		oppgbas.1	⊢ 𝑂 = ( oppg ‘ 𝑅 )
2		oppgtset.2	⊢ 𝐽 = ( TopSet ‘ 𝑅 )
3		df-tset	⊢ TopSet = Slot 9
4		9nn	⊢ 9 ∈ ℕ
5		2re	⊢ 2 ∈ ℝ
6		2lt9	⊢ 2 < 9
7	5 6	gtneii	⊢ 9 ≠ 2
8	1 3 4 7	oppglem	⊢ ( TopSet ‘ 𝑅 ) = ( TopSet ‘ 𝑂 )
9	2 8	eqtri	⊢ 𝐽 = ( TopSet ‘ 𝑂 )