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Theorem ifnot 3769
 Description: Negating the first argument swaps the last two arguments of a conditional operator. (Contributed by NM, 21-Jun-2007.)
Assertion
Ref Expression
ifnot

Proof of Theorem ifnot
StepHypRef Expression
1 notnot1 116 . . . 4
2 iffalse 3738 . . . 4
31, 2syl 16 . . 3
4 iftrue 3737 . . 3
53, 4eqtr4d 2470 . 2
6 iftrue 3737 . . 3
7 iffalse 3738 . . 3
86, 7eqtr4d 2470 . 2
95, 8pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1652  cif 3731 This theorem is referenced by:  sadadd2lem2  12954  tmsxpsval2  18561  itg2uba  19627  lgsneg  21095  lgsdilem  21098  itgaddnclem2  26254 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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