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Metamath Proof Explorer

Theorem basendxltdsndx

Description: The index of the slot for the base set is less than the index of the slot for the distance in an extensible structure. Formerly part of proof for tmslem . (Contributed by AV, 28-Oct-2024)

		Ref	Expression
	Assertion	basendxltdsndx	$⊢ {Base}_{ndx} < dist (ndx)$

Proof

Step	Hyp	Ref	Expression
1		1nn	$⊢ 1 \in ℕ$
2		2nn0	$⊢ 2 \in ℕ_{0}$
3		1nn0	$⊢ 1 \in ℕ_{0}$
4		1lt10	$⊢ 1 < 10$
5	1 2 3 4	declti	$⊢ 1 < 12$
6		basendx	$⊢ {Base}_{ndx} = 1$
7		dsndx	$⊢ dist (ndx) = 12$
8	5 6 7	3brtr4i	$⊢ {Base}_{ndx} < dist (ndx)$