Theorem nfiota1 5098

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 5097	. 2 |- ( iota x ph ) = U. { y | A. x ( ph <-> x = y ) }
2		nfaba1 2288	. . 3 |- F/_ x { y | A. x ( ph <-> x = y ) }
3	2	nfuni 3750	. 2 |- F/_ x U. { y | A. x ( ph <-> x = y ) }
4	1, 3	nfcxfr 2279	1 |- F/_ x ( iota x ph )

Syntax hints:   <-> wb 104   A.wal 1330   {cab 2126   F/_wnfc 2269   U.cuni 3744   iotacio 5094

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-sn 3538  df-uni 3745  df-iota 5096

This theorem is referenced by:  iota2df  5120  sniota  5123  nfriota1  5745  erovlem  6529