Theorem nfriota1 5495

Description: The abstraction variable in a restricted iota descriptor isn't free. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)

Assertion

Ref	Expression
nfriota1	|- F/_ x ( iota_ x e. A ph )

Distinct variable group:   x, A

Allowed substitution hint:   ph( x)

Proof of Theorem nfriota1

Step	Hyp	Ref	Expression
1		df-riota 5488	. 2 |- ( iota_ x e. A ph ) = ( iota x ( x e. A /\ ph ) )
2		nfiota1 4889	. 2 |- F/_ x ( iota x ( x e. A /\ ph ) )
3	1, 2	nfcxfr 2216	1 |- F/_ x ( iota_ x e. A ph )

Syntax hints:   /\ wa 102   e. wcel 1433   F/_wnfc 2206   iotacio 4885   iota_crio 5487

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-sn 3404  df-uni 3602  df-iota 4887  df-riota 5488

This theorem is referenced by:  riotaprop  5511  riotass2  5514  riotass  5515  lble  8025  oddpwdclemdvds  10548  oddpwdclemndvds  10549