Theorem nfiotaw 5100

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

Hypothesis

Ref	Expression
nfiotaw.1	|- F/ x ph

Assertion

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

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem nfiotaw

Step	Hyp	Ref	Expression
1		nftru 1443	. . 3 |- F/ y T.
2		nfiotaw.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfiotadw 5099	. 2 |- ( T. -> F/_ x ( iota y ph ) )
5	4	mptru 1341	1 |- F/_ x ( iota y ph )

Syntax hints:   T. wtru 1333   F/wnf 1437   F/_wnfc 2269   iotacio 5094

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-sn 3538  df-uni 3745  df-iota 5096

This theorem is referenced by:  csbiotag  5124  nffv  5439  nfsum1  11157  nfsum  11158  nfcprod1  11355  nfcprod  11356