Theorem starvndxnplusgndx

Description: The slot for the involution function is not the slot for the base set in an extensible structure. Formerly part of proof for ressstarv . (Contributed by AV, 18-Oct-2024)

	Ref	Expression
Assertion	starvndxnplusgndx	⊢ ( *𝑟 ‘ ndx ) ≠ ( +g ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		2re	⊢ 2 ∈ ℝ
2		2lt4	⊢ 2 < 4
3	1 2	gtneii	⊢ 4 ≠ 2
4		starvndx	⊢ ( *𝑟 ‘ ndx ) = 4
5		plusgndx	⊢ ( +g ‘ ndx ) = 2
6	4 5	neeq12i	⊢ ( ( *𝑟 ‘ ndx ) ≠ ( +g ‘ ndx ) ↔ 4 ≠ 2 )
7	3 6	mpbir	⊢ ( *𝑟 ‘ ndx ) ≠ ( +g ‘ ndx )