Theorem riotav 6044

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 6038	. 2 |- ( iota_ x e. _V ph ) = ( iota x ( x e. _V /\ ph ) )
2		vex 2824	. . . 4 |- x e. _V
3	2	biantrur 303	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	iotabii 5361	. 2 |- ( iota x ph ) = ( iota x ( x e. _V /\ ph ) )
5	1, 4	eqtr4i 2262	1 |- ( iota_ x e. _V ph ) = ( iota x ph )

This proof depends on syntax axioms:   /\ wa 104   = wceq 1402   e. wcel 2209   _Vcvv 2821   iotacio 5335   iota_crio 6037

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-v 2823  df-uni 3936  df-iota 5337  df-riota 6038

This theorem is used by: (None)