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Theorem iota5 5569
 Description: A method for computing iota. (Contributed by NM, 17-Sep-2013.)
Hypothesis
Ref Expression
iota5.1
Assertion
Ref Expression
iota5
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iota5
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 iota5.1 . . 3
21alrimiv 1695 . 2
3 eqeq2 2482 . . . . . . 7
43bibi2d 318 . . . . . 6
54albidv 1689 . . . . 5
6 eqeq2 2482 . . . . 5
75, 6imbi12d 320 . . . 4
8 iotaval 5560 . . . 4
97, 8vtoclg 3171 . . 3
109adantl 466 . 2
112, 10mpd 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1377   wceq 1379   wcel 1767  cio 5547 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2820  df-v 3115  df-sbc 3332  df-un 3481  df-sn 4028  df-pr 4030  df-uni 4246  df-iota 5549 This theorem is referenced by:  isf32lem9  8737  rlimdm  13333  fsum  13501  gsumval2a  15825  dchrptlem1  23267  lgsdchrval  23350  fprod  28650  rlimdmafv  31729
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