Metamath Proof Explorer


Theorem starvndxnbasendx

Description: The slot for the involution function is not the slot for the base set in an extensible structure. Formerly part of proof for ressstarv . (Contributed by AV, 18-Oct-2024)

Ref Expression
Assertion starvndxnbasendx
|- ( *r ` ndx ) =/= ( Base ` ndx )

Proof

Step Hyp Ref Expression
1 1re
 |-  1 e. RR
2 1lt4
 |-  1 < 4
3 1 2 gtneii
 |-  4 =/= 1
4 starvndx
 |-  ( *r ` ndx ) = 4
5 basendx
 |-  ( Base ` ndx ) = 1
6 4 5 neeq12i
 |-  ( ( *r ` ndx ) =/= ( Base ` ndx ) <-> 4 =/= 1 )
7 3 6 mpbir
 |-  ( *r ` ndx ) =/= ( Base ` ndx )