Theorem basendxlttsetndx

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

	Ref	Expression
Assertion	basendxlttsetndx	⊢ ( Base ‘ ndx ) < ( TopSet ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		1lt9	⊢ 1 < 9
2		basendx	⊢ ( Base ‘ ndx ) = 1
3		tsetndx	⊢ ( TopSet ‘ ndx ) = 9
4	1 2 3	3brtr4i	⊢ ( Base ‘ ndx ) < ( TopSet ‘ ndx )