Theorem tsetndxnstarvndx

Description: The slot for the topology is not the slot for the involution in an extensible structure. Formerly part of proof for cnfldfun . (Contributed by AV, 11-Nov-2024)

	Ref	Expression
Assertion	tsetndxnstarvndx	⊢ ( TopSet ‘ ndx ) ≠ ( *𝑟 ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		4re	⊢ 4 ∈ ℝ
2		4lt9	⊢ 4 < 9
3	1 2	gtneii	⊢ 9 ≠ 4
4		tsetndx	⊢ ( TopSet ‘ ndx ) = 9
5		starvndx	⊢ ( *𝑟 ‘ ndx ) = 4
6	4 5	neeq12i	⊢ ( ( TopSet ‘ ndx ) ≠ ( *𝑟 ‘ ndx ) ↔ 9 ≠ 4 )
7	3 6	mpbir	⊢ ( TopSet ‘ ndx ) ≠ ( *𝑟 ‘ ndx )