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Theorem ifbi 3748
 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 864 . 2
2 iftrue 3737 . . . 4
3 iftrue 3737 . . . . 5
43eqcomd 2440 . . . 4
52, 4sylan9eq 2487 . . 3
6 iffalse 3738 . . . 4
7 iffalse 3738 . . . . 5
87eqcomd 2440 . . . 4
96, 8sylan9eq 2487 . . 3
105, 9jaoi 369 . 2
111, 10sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359   wceq 1652  cif 3731 This theorem is referenced by:  ifbid  3749  ifbieq2i  3750  dchrhash  21045  lgsdi  21106  rpvmasum2  21196  itg2gt0cn  26223 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-if 3732
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