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Theorem ifbieq2i 3681
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 3679 . . 3
31, 2ax-mp 8 . 2
4 ifbieq2i.2 . . 3
5 ifeq2 3667 . . 3
64, 5ax-mp 8 . 2
73, 6eqtri 2373 1
Colors of variables: wff setvar class
Syntax hints:   wb 176   wceq 1642  cif 3662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-if 3663
This theorem is referenced by:  ifbieq12i  3683
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