Theorem riotav 5907

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 5901	. 2 |- ( iota_ x e. _V ph ) = ( iota x ( x e. _V /\ ph ) )
2		vex 2775	. . . 4 |- x e. _V
3	2	biantrur 303	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	iotabii 5256	. 2 |- ( iota x ph ) = ( iota x ( x e. _V /\ ph ) )
5	1, 4	eqtr4i 2229	1 |- ( iota_ x e. _V ph ) = ( iota x ph )

Syntax hints:   /\ wa 104   = wceq 1373   e. wcel 2176   _Vcvv 2772   iotacio 5231   iota_crio 5900

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rex 2490  df-v 2774  df-uni 3851  df-iota 5233  df-riota 5901

This theorem is referenced by: (None)