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Theorem ifbieq12i 3967
 Description: Equivalence deduction for conditional operators. (Contributed by NM, 18-Mar-2013.)
Hypotheses
Ref Expression
ifbieq12i.1
ifbieq12i.2
ifbieq12i.3
Assertion
Ref Expression
ifbieq12i

Proof of Theorem ifbieq12i
StepHypRef Expression
1 ifbieq12i.2 . . 3
2 ifeq1 3945 . . 3
31, 2ax-mp 5 . 2
4 ifbieq12i.1 . . 3
5 ifbieq12i.3 . . 3
64, 5ifbieq2i 3965 . 2
73, 6eqtri 2486 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  =wceq 1395  ifcif 3941 This theorem is referenced by:  cbvditg  22258  sgnneg  28479  binomcxplemdvsum  31260 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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-un 3480  df-if 3942
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