Theorem cbviotav 5089

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 1508	. 2 |- F/ y ph
3		nfv 1508	. 2 |- F/ x ps
4	1, 2, 3	cbviota 5088	1 |- ( iota x ph ) = ( iota y ps )

Syntax hints:   -> wi 4   <-> wb 104   = wceq 1331   iotacio 5081

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-sn 3528  df-uni 3732  df-iota 5083

This theorem is referenced by: (None)