Theorem nfiotaw 5297

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 1515	. . 3 |- F/ y T.
2		nfiotaw.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfiotadw 5296	. 2 |- ( T. -> F/_ x ( iota y ph ) )
5	4	mptru 1407	1 |- F/_ x ( iota y ph )

Syntax hints:   T. wtru 1399   F/wnf 1509   F/_wnfc 2362   iotacio 5291

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

This theorem is referenced by:  csbiotag  5326  nffv  5658  nfsum1  11996  nfsum  11997  nfcprod1  12195  nfcprod  12196