Theorem riotav 5960

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 5954	. 2 |- ( iota_ x e. _V ph ) = ( iota x ( x e. _V /\ ph ) )
2		vex 2802	. . . 4 |- x e. _V
3	2	biantrur 303	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	iotabii 5302	. 2 |- ( iota x ph ) = ( iota x ( x e. _V /\ ph ) )
5	1, 4	eqtr4i 2253	1 |- ( iota_ x e. _V ph ) = ( iota x ph )

Syntax hints:   /\ wa 104   = wceq 1395   e. wcel 2200   _Vcvv 2799   iotacio 5276   iota_crio 5953

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rex 2514  df-v 2801  df-uni 3889  df-iota 5278  df-riota 5954

This theorem is referenced by: (None)