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Theorem riotabidva 6337
 Description: Equivalent wff's yield equal restricted class abstractions (deduction rule). (rabbidva 2792 analog.) (Contributed by NM, 17-Jan-2012.)
Hypothesis
Ref Expression
riotabidva.1
Assertion
Ref Expression
riotabidva
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riotabidva
StepHypRef Expression
1 riotabidva.1 . . . . . . 7
21pm5.32da 622 . . . . . 6
32iotabidv 5256 . . . . 5
43adantr 451 . . . 4
54ifeq1da 3603 . . 3
61reubidva 2736 . . . 4
76ifbid 3596 . . 3
85, 7eqtrd 2328 . 2
9 df-riota 6320 . 2
10 df-riota 6320 . 2
118, 9, 103eqtr4g 2353 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1632   wcel 1696  cab 2282  wreu 2558  cif 3578  cio 5233  cfv 5271  cund 6312  crio 6313 This theorem is referenced by:  riotabiia  6338  cidpropd  13629  grpinvpropd  14559  grpoidval  20899  adjval2  22487  xdivval  23118  issubcv  25773  glbconN  30188  cdlemk33N  31720  cdlemk34  31721  cdlemkid4  31745 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-reu 2563  df-rab 2565  df-v 2803  df-un 3170  df-if 3579  df-uni 3844  df-iota 5235  df-riota 6320
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