Theorem nfiotaxy 4891

Description: Bound-variable hypothesis builder for the iota class. (Contributed by NM, 23-Aug-2011.)

Hypothesis

Ref	Expression
nfiota.1	|- F/ x ph

Assertion

Ref	Expression
nfiotaxy	|- F/_ x ( iota y ph )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem nfiotaxy

Step	Hyp	Ref	Expression
1		nftru 1395	. . 3 |- F/ y T.
2		nfiota.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfiotadxy 4890	. 2 |- ( T. -> F/_ x ( iota y ph ) )
5	4	trud 1293	1 |- F/_ x ( iota y ph )

Syntax hints:   T. wtru 1285   F/wnf 1389   F/_wnfc 2206   iotacio 4885

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

This theorem is referenced by:  csbiotag  4915  nffv  5205  nfsum1  10193  nfsum  10194