Theorem starvndxnbasendx

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	starvndxnbasendx	$$⊢{\mathrm{*}}_{\mathrm{ndx}}\ne {\mathrm{Base}}_{\mathrm{ndx}}$$

Proof

Step	Hyp	Ref	Expression
1		1re	$$⊢1\in ℝ$$
2		1lt4	$$⊢1<4$$
3	1 2	gtneii	$$⊢4\ne 1$$
4		starvndx	$$⊢{\mathrm{*}}_{\mathrm{ndx}}=4$$
5		basendx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}=1$$
6	4 5	neeq12i	$$⊢{\mathrm{*}}_{\mathrm{ndx}}\ne {\mathrm{Base}}_{\mathrm{ndx}}\leftrightarrow 4\ne 1$$
7	3 6	mpbir	$$⊢{\mathrm{*}}_{\mathrm{ndx}}\ne {\mathrm{Base}}_{\mathrm{ndx}}$$