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Theorem iota5 4887
 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 1754 . 2
3 eqeq2 2049 . . . . . . 7
43bibi2d 221 . . . . . 6
54albidv 1705 . . . . 5
6 eqeq2 2049 . . . . 5
75, 6imbi12d 223 . . . 4
8 iotaval 4878 . . . 4
97, 8vtoclg 2613 . . 3
109adantl 262 . 2
112, 10mpd 13 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243   wcel 1393  cio 4865 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-sn 3381  df-pr 3382  df-uni 3581  df-iota 4867 This theorem is referenced by: (None)
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