Theorem nfiotaw 5223

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 1480	. . 3 |- F/ y T.
2		nfiotaw.1	. . . 4 |- F/ x ph
3	2	a1i 9	. . 3 |- ( T. -> F/ x ph )
4	1, 3	nfiotadw 5222	. 2 |- ( T. -> F/_ x ( iota y ph ) )
5	4	mptru 1373	1 |- F/_ x ( iota y ph )

Syntax hints:   T. wtru 1365   F/wnf 1474   F/_wnfc 2326   iotacio 5217

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-sn 3628  df-uni 3840  df-iota 5219

This theorem is referenced by:  csbiotag  5251  nffv  5568  nfsum1  11505  nfsum  11506  nfcprod1  11703  nfcprod  11704