Theorem nfriota1 5989

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 5981	. 2 |- ( iota_ x e. A ph ) = ( iota x ( x e. A /\ ph ) )
2		nfiota1 5295	. 2 |- F/_ x ( iota x ( x e. A /\ ph ) )
3	1, 2	nfcxfr 2372	1 |- F/_ x ( iota_ x e. A ph )

Syntax hints:   /\ wa 104   e. wcel 2202   F/_wnfc 2362   iotacio 5291   iota_crio 5980

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-sn 3679  df-uni 3899  df-iota 5293  df-riota 5981

This theorem is referenced by:  riotaprop  6007  riotass2  6010  riotass  6011  lble  9186  oddpwdclemdvds  12822  oddpwdclemndvds  12823