Metamath Proof Explorer


Theorem cbviotav

Description: Change bound variables in a description binder. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbviotavw when possible. (Contributed by Andrew Salmon, 1-Aug-2011) (New usage is discouraged.)

Ref Expression
Hypothesis cbviotav.1
|- ( x = y -> ( ph <-> ps ) )
Assertion cbviotav
|- ( iota x ph ) = ( iota y ps )

Proof

Step Hyp Ref Expression
1 cbviotav.1
 |-  ( x = y -> ( ph <-> ps ) )
2 nfv
 |-  F/ y ph
3 nfv
 |-  F/ x ps
4 1 2 3 cbviota
 |-  ( iota x ph ) = ( iota y ps )