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 e. NN
2 8nn0
 |-  8 e. NN0
3 1nn0
 |-  1 e. NN0
4 1lt10
 |-  1 < ; 1 0
5 1 2 3 4 declti
 |-  1 < ; 1 8
6 basendx
 |-  ( Base ` ndx ) = 1
7 edgfndx
 |-  ( .ef ` ndx ) = ; 1 8
8 5 6 7 3brtr4i
 |-  ( Base ` ndx ) < ( .ef ` ndx )