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Theorem ifbieq2i 3495
 Description: Equivalence/equality inference for conditional operators. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypotheses
Ref Expression
ifbieq2i.1
ifbieq2i.2
Assertion
Ref Expression
ifbieq2i

Proof of Theorem ifbieq2i
StepHypRef Expression
1 ifbieq2i.1 . . 3
2 ifbi 3492 . . 3
31, 2ax-mp 5 . 2
4 ifbieq2i.2 . . 3
5 ifeq2 3478 . . 3
64, 5ax-mp 5 . 2
73, 6eqtri 2160 1
 Colors of variables: wff set class Syntax hints:   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:  ifbieq12i  3497  gcdcom  11662  gcdass  11703  lcmcom  11745  lcmass  11766
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