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Theorem riota5f 6282
Description: A method for computing restricted iota. (Contributed by NM, 16-Apr-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
riota5f.1
riota5f.2
riota5f.3
Assertion
Ref Expression
riota5f
Distinct variable groups:   ,   ,

Proof of Theorem riota5f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 riota5f.3 . . 3
21ralrimiva 2871 . 2
3 riota5f.2 . . . 4
4 a1tru 1411 . . . . . . 7
5 reu6i 3290 . . . . . . . . 9
65adantl 466 . . . . . . . 8
7 nfv 1707 . . . . . . . . . 10
8 nfv 1707 . . . . . . . . . . 11
9 nfra1 2838 . . . . . . . . . . 11
108, 9nfan 1928 . . . . . . . . . 10
117, 10nfan 1928 . . . . . . . . 9
12 nfcvd 2620 . . . . . . . . 9
13 nfvd 1708 . . . . . . . . 9
14 simprl 756 . . . . . . . . 9
15 simpr 461 . . . . . . . . . . 11
16 simplrr 762 . . . . . . . . . . . 12
17 simplrl 761 . . . . . . . . . . . . 13
1815, 17eqeltrd 2545 . . . . . . . . . . . 12
19 rsp 2823 . . . . . . . . . . . 12
2016, 18, 19sylc 60 . . . . . . . . . . 11
2115, 20mpbird 232 . . . . . . . . . 10
22 a1tru 1411 . . . . . . . . . 10
2321, 222thd 240 . . . . . . . . 9
2411, 12, 13, 14, 23riota2df 6278 . . . . . . . 8
256, 24mpdan 668 . . . . . . 7
264, 25mpbid 210 . . . . . 6
2726expr 615 . . . . 5
2827ralrimiva 2871 . . . 4
29 rspsbc 3417 . . . 4
303, 28, 29sylc 60 . . 3
31 nfcvd 2620 . . . . . . . 8
32 riota5f.1 . . . . . . . 8
3331, 32nfeqd 2626 . . . . . . 7
347, 33nfan1 1927 . . . . . 6
35 simpr 461 . . . . . . . 8
3635eqeq2d 2471 . . . . . . 7
3736bibi2d 318 . . . . . 6
3834, 37ralbid 2891 . . . . 5
3935eqeq2d 2471 . . . . 5
4038, 39imbi12d 320 . . . 4
413, 40sbcied 3364 . . 3
4230, 41mpbid 210 . 2
432, 42mpd 15 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395   wtru 1396  e.wcel 1818  F/_wnfc 2605  A.wral 2807  E!wreu 2809  [.wsbc 3327  iota_crio 6256
This theorem is referenced by:  riota5  6283
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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257
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