Theorem cbviotav 5293

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 1576	. 2 |- F/ y ph
3		nfv 1576	. 2 |- F/ x ps
4	1, 2, 3	cbviota 5291	1 |- ( iota x ph ) = ( iota y ps )

Syntax hints:   -> wi 4   <-> wb 105   = wceq 1397   iotacio 5284

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-sn 3675  df-uni 3894  df-iota 5286

This theorem is referenced by: (None)