Theorem riotav 5928

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 5922	. 2 |- ( iota_ x e. _V ph ) = ( iota x ( x e. _V /\ ph ) )
2		vex 2779	. . . 4 |- x e. _V
3	2	biantrur 303	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	iotabii 5274	. 2 |- ( iota x ph ) = ( iota x ( x e. _V /\ ph ) )
5	1, 4	eqtr4i 2231	1 |- ( iota_ x e. _V ph ) = ( iota x ph )

Syntax hints:   /\ wa 104   = wceq 1373   e. wcel 2178   _Vcvv 2776   iotacio 5249   iota_crio 5921

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rex 2492  df-v 2778  df-uni 3865  df-iota 5251  df-riota 5922

This theorem is referenced by: (None)