Theorem nfiotaw 5200

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 1477	. . 3 |- F/ y T.
2		nfiotaw.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfiotadw 5199	. 2 |- ( T. -> F/_ x ( iota y ph ) )
5	4	mptru 1373	1 |- F/_ x ( iota y ph )

Syntax hints:   T. wtru 1365   F/wnf 1471   F/_wnfc 2319   iotacio 5194

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-sn 3613  df-uni 3825  df-iota 5196

This theorem is referenced by:  csbiotag  5228  nffv  5544  nfsum1  11395  nfsum  11396  nfcprod1  11593  nfcprod  11594