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Theorem ifbi 3679
 Description: Equivalence theorem for conditional operators. (Contributed by Raph Levien, 15-Jan-2004.)
Assertion
Ref Expression
ifbi

Proof of Theorem ifbi
StepHypRef Expression
1 dfbi3 863 . 2
2 iftrue 3668 . . . 4
3 iftrue 3668 . . . . 5
43eqcomd 2358 . . . 4
52, 4sylan9eq 2405 . . 3
6 iffalse 3669 . . . 4
7 iffalse 3669 . . . . 5
87eqcomd 2358 . . . 4
96, 8sylan9eq 2405 . . 3
105, 9jaoi 368 . 2
111, 10sylbi 187 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358   wceq 1642  cif 3662 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-if 3663 This theorem is referenced by:  ifbid  3680  ifbieq2i  3681
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