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Theorem ifbi 3962
 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 893 . 2
2 iftrue 3947 . . . 4
3 iftrue 3947 . . . . 5
43eqcomd 2465 . . . 4
52, 4sylan9eq 2518 . . 3
6 iffalse 3950 . . . 4
7 iffalse 3950 . . . . 5
87eqcomd 2465 . . . 4
96, 8sylan9eq 2518 . . 3
105, 9jaoi 379 . 2
111, 10sylbi 195 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  ifcif 3941 This theorem is referenced by:  ifbid  3963  ifbieq2i  3965  gsummoncoe1  18346  scmatscm  19015  mulmarep1gsum1  19075  madugsum  19145  mp2pm2mplem4  19310  dchrhash  23546  lgsdi  23607  rpvmasum2  23697  itg2gt0cn  30070  bj-projval  34554  elimhyps  34692  dedths  34693 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-if 3942
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