Theorem nfiota1 5239

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 5238	. 2 |- ( iota x ph ) = U. { y | A. x ( ph <-> x = y ) }
2		nfaba1 2355	. . 3 |- F/_ x { y | A. x ( ph <-> x = y ) }
3	2	nfuni 3858	. 2 |- F/_ x U. { y | A. x ( ph <-> x = y ) }
4	1, 3	nfcxfr 2346	1 |- F/_ x ( iota x ph )

Syntax hints:   <-> wb 105   A.wal 1371   {cab 2192   F/_wnfc 2336   U.cuni 3852   iotacio 5235

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 2188

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-rex 2491  df-sn 3640  df-uni 3853  df-iota 5237

This theorem is referenced by:  iota2df  5262  sniota  5267  nfriota1  5914  erovlem  6721