Theorem cbviotav 4873

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 1421	. 2 |- F/ y ph
3		nfv 1421	. 2 |- F/ x ps
4	1, 2, 3	cbviota 4872	1 |- ( iota x ph ) = ( iota y ps )

Syntax hints:   -> wi 4   <-> wb 98   = wceq 1243   iotacio 4865

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-sn 3381  df-uni 3581  df-iota 4867

This theorem is referenced by: (None)