Theorem nfriota1 5805

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 5798	. 2 |- ( iota_ x e. A ph ) = ( iota x ( x e. A /\ ph ) )
2		nfiota1 5155	. 2 |- F/_ x ( iota x ( x e. A /\ ph ) )
3	1, 2	nfcxfr 2305	1 |- F/_ x ( iota_ x e. A ph )

Syntax hints:   /\ wa 103   e. wcel 2136   F/_wnfc 2295   iotacio 5151   iota_crio 5797

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rex 2450  df-sn 3582  df-uni 3790  df-iota 5153  df-riota 5798

This theorem is referenced by:  riotaprop  5821  riotass2  5824  riotass  5825  lble  8842  oddpwdclemdvds  12102  oddpwdclemndvds  12103