Theorem cbviotav 5857

Description: Change bound variables in a description binder. (Contributed by Andrew Salmon, 1-Aug-2011.)

Hypothesis

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

Assertion

Ref	Expression
cbviotav	|- ( iota x ph ) = ( iota y ps )

Distinct variable groups:   ph, y   ps, x

Allowed substitution hints:   ph( x)   ps( y)

Proof of Theorem cbviotav

Step	Hyp	Ref	Expression
1		cbviotav.1	. 2 |- ( x = y -> ( ph <-> ps ) )
2		nfv 1843	. 2 |- F/ y ph
3		nfv 1843	. 2 |- F/ x ps
4	1, 2, 3	cbviota 5856	1 |- ( iota x ph ) = ( iota y ps )

Syntax hints:   -> wi 4   <-> wb 196   = wceq 1483   iotacio 5849

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rex 2918  df-sn 4178  df-uni 4437  df-iota 5851

This theorem is referenced by:  oeeui  7682  ellimciota  39846  fourierdlem96  40419  fourierdlem97  40420  fourierdlem98  40421  fourierdlem99  40422  fourierdlem105  40428  fourierdlem106  40429  fourierdlem108  40431  fourierdlem110  40433  fourierdlem112  40435  fourierdlem113  40436  fourierdlem115  40438