Theorem nfriotad 6265

Description: Deduction version of nfriota 6266. (Contributed by NM, 18-Feb-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)

Hypotheses

Ref	Expression
nfriotad.1
nfriotad.2
nfriotad.3

Assertion

Ref	Expression
nfriotad

Proof of Theorem nfriotad

Step	Hyp	Ref	Expression
1		df-riota 6257	. 2
2		nfriotad.1	. . . . . 6
3		nfnae 2058	. . . . . 6
4	2, 3	nfan 1928	. . . . 5
5		nfcvf 2644	. . . . . . . 8
6	5	adantl 466	. . . . . . 7
7		nfriotad.3	. . . . . . . 8
8	7	adantr 465	. . . . . . 7
9	6, 8	nfeld 2627	. . . . . 6
10		nfriotad.2	. . . . . . 7
11	10	adantr 465	. . . . . 6
12	9, 11	nfand 1925	. . . . 5
13	4, 12	nfiotad 5559	. . . 4
14	13	ex 434	. . 3
15		nfiota1 5558	. . . 4
16		eqidd 2458	. . . . 5
17	16	drnfc1 2638	. . . 4
18	15, 17	mpbiri 233	. . 3
19	14, 18	pm2.61d2 160	. 2
20	1, 19	nfcxfrd 2618	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  iotacio 5554  iota_crio 6256

This theorem is referenced by:  nfriota  6266

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  df-riota 6257