Theorem baseltedgf

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

	Ref	Expression
Assertion	baseltedgf	⊢ ( Base ‘ ndx ) < ( .ef ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		1nn	⊢ 1 ∈ ℕ
2		8nn0	⊢ 8 ∈ ℕ0
3		1nn0	⊢ 1 ∈ ℕ0
4		1lt10	⊢ 1 < ; 1 0
5	1 2 3 4	declti	⊢ 1 < ; 1 8
6		df-base	⊢ Base = Slot 1
7	6 1	ndxarg	⊢ ( Base ‘ ndx ) = 1
8		df-edgf	⊢ .ef = Slot ; 1 8
9		8nn	⊢ 8 ∈ ℕ
10	3 9	decnncl	⊢ ; 1 8 ∈ ℕ
11	8 10	ndxarg	⊢ ( .ef ‘ ndx ) = ; 1 8
12	5 7 11	3brtr4i	⊢ ( Base ‘ ndx ) < ( .ef ‘ ndx )