Theorem nfiota1 5339

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 5338	. 2 |- ( iota x ph ) = U. { y | A. x ( ph <-> x = y ) }
2		nfaba1 2398	. . 3 |- F/_ x { y | A. x ( ph <-> x = y ) }
3	2	nfuni 3941	. 2 |- F/_ x U. { y | A. x ( ph <-> x = y ) }
4	1, 3	nfcxfr 2389	1 |- F/_ x ( iota x ph )

This proof depends on syntax axioms:   <-> wb 105   A.wal 1400   {cab 2224   F/_wnfc 2379   U.cuni 3935   iotacio 5335

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-sn 3715  df-uni 3936  df-iota 5337

This theorem is used by:  iota2df  5363  sniota  5368  nfriota1  6046  erovlem  6901