Theorem nfiota1 5279

Description: Bound-variable hypothesis builder for the iota class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)

Assertion

Ref	Expression
nfiota1	|- F/_ x ( iota x ph )

Proof of Theorem nfiota1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfiota2 5278	. 2 |- ( iota x ph ) = U. { y | A. x ( ph <-> x = y ) }
2		nfaba1 2378	. . 3 |- F/_ x { y | A. x ( ph <-> x = y ) }
3	2	nfuni 3893	. 2 |- F/_ x U. { y | A. x ( ph <-> x = y ) }
4	1, 3	nfcxfr 2369	1 |- F/_ x ( iota x ph )

Syntax hints:   <-> wb 105   A.wal 1393   {cab 2215   F/_wnfc 2359   U.cuni 3887   iotacio 5275

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-sn 3672  df-uni 3888  df-iota 5277

This theorem is referenced by:  iota2df  5303  sniota  5308  nfriota1  5961  erovlem  6772