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Theorem iota5 4830
Description: A method for computing iota. (Contributed by NM, 17-Sep-2013.)
Hypothesis
Ref Expression
iota5.1  V
Assertion
Ref Expression
iota5  V  iota
Distinct variable groups:   ,   , V   ,
Allowed substitution hint:   ()

Proof of Theorem iota5
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 iota5.1 . . 3  V
21alrimiv 1751 . 2  V
3 eqeq2 2046 . . . . . . 7
43bibi2d 221 . . . . . 6
54albidv 1702 . . . . 5
6 eqeq2 2046 . . . . 5  iota  iota
75, 6imbi12d 223 . . . 4  iota  iota
8 iotaval 4821 . . . 4  iota
97, 8vtoclg 2607 . . 3  V  iota
109adantl 262 . 2  V  iota
112, 10mpd 13 1  V  iota
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242   wcel 1390   iotacio 4808
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-sbc 2759  df-un 2916  df-sn 3373  df-pr 3374  df-uni 3572  df-iota 4810
This theorem is referenced by: (None)
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