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Theorem ifbi 3927
 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 901 . 2
2 iftrue 3912 . . . 4
3 iftrue 3912 . . . . 5
43eqcomd 2428 . . . 4
52, 4sylan9eq 2481 . . 3
6 iffalse 3915 . . . 4
7 iffalse 3915 . . . . 5
87eqcomd 2428 . . . 4
96, 8sylan9eq 2481 . . 3
105, 9jaoi 380 . 2
111, 10sylbi 198 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wo 369   wa 370   wceq 1437  cif 3906 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-if 3907 This theorem is referenced by:  ifbid  3928  ifbieq2i  3930  gsummoncoe1  18826  scmatscm  19462  mulmarep1gsum1  19522  madugsum  19592  mp2pm2mplem4  19757  dchrhash  24088  lgsdi  24149  rpvmasum2  24239  bj-projval  31365  itg2gt0cn  31730  elimhyps  32271  dedths  32272
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