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Theorem ifbieq12d 3498
 Description: Equivalence deduction for conditional operators. (Contributed by Jeff Madsen, 2-Sep-2009.)
Hypotheses
Ref Expression
ifbieq12d.1
ifbieq12d.2
ifbieq12d.3
Assertion
Ref Expression
ifbieq12d

Proof of Theorem ifbieq12d
StepHypRef Expression
1 ifbieq12d.1 . . 3
21ifbid 3493 . 2
3 ifbieq12d.2 . . 3
4 ifbieq12d.3 . . 3
53, 4ifeq12d 3491 . 2
62, 5eqtrd 2172 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1331  cif 3474 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rab 2425  df-v 2688  df-un 3075  df-if 3475 This theorem is referenced by:  updjudhcoinlf  6965  updjudhcoinrg  6966  omp1eom  6980  xaddval  9640  iseqf1olemqval  10272  iseqf1olemqk  10279  seq3f1olemqsum  10285  exp3val  10307  cvgratz  11313  eucalgval2  11745  ennnfonelemg  11927  ennnfonelem1  11931  ressid2  12032  ressval2  12033
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