Theorem nfriota1 5615

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 5608	. 2 |- ( iota_ x e. A ph ) = ( iota x ( x e. A /\ ph ) )
2		nfiota1 4982	. 2 |- F/_ x ( iota x ( x e. A /\ ph ) )
3	1, 2	nfcxfr 2225	1 |- F/_ x ( iota_ x e. A ph )

Syntax hints:   /\ wa 102   e. wcel 1438   F/_wnfc 2215   iotacio 4978   iota_crio 5607

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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-sn 3452  df-uni 3654  df-iota 4980  df-riota 5608

This theorem is referenced by:  riotaprop  5631  riotass2  5634  riotass  5635  lble  8408  oddpwdclemdvds  11426  oddpwdclemndvds  11427