Theorem basendxlttsetndx

Description: The index of the slot for the base set is less than the index of the slot for the topology in an extensible structure. (Contributed by AV, 31-Oct-2024)

	Ref	Expression
Assertion	basendxlttsetndx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<\mathrm{TopSet}\left(\mathrm{ndx}\right)$$

Proof

Step	Hyp	Ref	Expression
1		1lt9	$$⊢1<9$$
2		basendx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}=1$$
3		tsetndx	$$⊢\mathrm{TopSet}\left(\mathrm{ndx}\right)=9$$
4	1 2 3	3brtr4i	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<\mathrm{TopSet}\left(\mathrm{ndx}\right)$$