Theorem nfriota1 5930

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 5922	. 2 |- ( iota_ x e. A ph ) = ( iota x ( x e. A /\ ph ) )
2		nfiota1 5253	. 2 |- F/_ x ( iota x ( x e. A /\ ph ) )
3	1, 2	nfcxfr 2347	1 |- F/_ x ( iota_ x e. A ph )

Syntax hints:   /\ wa 104   e. wcel 2178   F/_wnfc 2337   iotacio 5249   iota_crio 5921

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rex 2492  df-sn 3649  df-uni 3865  df-iota 5251  df-riota 5922

This theorem is referenced by:  riotaprop  5946  riotass2  5949  riotass  5950  lble  9055  oddpwdclemdvds  12607  oddpwdclemndvds  12608