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Metamath Proof Explorer

Theorem basendxltedgfndx

Description: The index value of the Base slot is less than the index value of the .ef slot. (Contributed by AV, 21-Sep-2020) (Proof shortened by AV, 30-Oct-2024)

		Ref	Expression
	Assertion	basendxltedgfndx	$⊢ {Base}_{ndx} < ef (ndx)$

Proof

Step	Hyp	Ref	Expression
1		1nn	$⊢ 1 \in ℕ$
2		8nn0	$⊢ 8 \in ℕ_{0}$
3		1nn0	$⊢ 1 \in ℕ_{0}$
4		1lt10	$⊢ 1 < 10$
5	1 2 3 4	declti	$⊢ 1 < 18$
6		basendx	$⊢ {Base}_{ndx} = 1$
7		edgfndx	$⊢ ef (ndx) = 18$
8	5 6 7	3brtr4i	$⊢ {Base}_{ndx} < ef (ndx)$