Theorem iota5 5576

Description: A method for computing iota. (Contributed by NM, 17-Sep-2013.)

Hypothesis

Ref	Expression
iota5.1

Assertion

Ref	Expression
iota5

Distinct variable groups:   ,   ,   ,

Proof of Theorem iota5

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		iota5.1	. . 3
2	1	alrimiv 1719	. 2
3		eqeq2 2472	. . . . . . 7
4	3	bibi2d 318	. . . . . 6
5	4	albidv 1713	. . . . 5
6		eqeq2 2472	. . . . 5
7	5, 6	imbi12d 320	. . . 4
8		iotaval 5567	. . . 4
9	7, 8	vtoclg 3167	. . 3
10	9	adantl 466	. 2
11	2, 10	mpd 15	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  iotacio 5554

This theorem is referenced by:  isf32lem9  8762  rlimdm  13374  fsum  13542  fprod  13748  gsumval2a  15906  dchrptlem1  23539  lgsdchrval  23622  rlimdmafv  32262

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-or 370  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-rex 2813  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556