Theorem riotav 5493

Description: An iota restricted to the universe is unrestricted. (Contributed by NM, 18-Sep-2011.)

Assertion

Ref	Expression
riotav	|- ( iota_ x e. _V ph ) = ( iota x ph )

Proof of Theorem riotav

Step	Hyp	Ref	Expression
1		df-riota 5488	. 2 |- ( iota_ x e. _V ph ) = ( iota x ( x e. _V /\ ph ) )
2		vex 2604	. . . 4 |- x e. _V
3	2	biantrur 297	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	iotabii 4909	. 2 |- ( iota x ph ) = ( iota x ( x e. _V /\ ph ) )
5	1, 4	eqtr4i 2104	1 |- ( iota_ x e. _V ph ) = ( iota x ph )

Syntax hints:   /\ wa 102   = wceq 1284   e. wcel 1433   _Vcvv 2601   iotacio 4885   iota_crio 5487

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-v 2603  df-uni 3602  df-iota 4887  df-riota 5488

This theorem is referenced by: (None)