Theorem nfiotad 5559

Description: Deduction version of nfiota 5560. (Contributed by NM, 18-Feb-2013.)

Hypotheses

Ref	Expression
nfiotad.1
nfiotad.2

Assertion

Ref	Expression
nfiotad

Proof of Theorem nfiotad

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfiota2 5557	. 2
2		nfv 1707	. . . 4
3		nfiotad.1	. . . . 5
4		nfiotad.2	. . . . . . 7
5	4	adantr 465	. . . . . 6
6		nfcvf 2644	. . . . . . . 8
7	6	adantl 466	. . . . . . 7
8		nfcvd 2620	. . . . . . 7
9	7, 8	nfeqd 2626	. . . . . 6
10	5, 9	nfbid 1933	. . . . 5
11	3, 10	nfald2 2073	. . . 4
12	2, 11	nfabd 2641	. . 3
13	12	nfunid 4256	. 2
14	1, 13	nfcxfrd 2618	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616  {cab 2442  F/_wnfc 2605  U.cuni 4249  iotacio 5554

This theorem is referenced by:  nfiota  5560  nfriotad  6265

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-sn 4030  df-uni 4250  df-iota 5556