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Theorem ifnot 3986
 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 122 . . . 4
21iffalsed 3952 . . 3
3 iftrue 3947 . . 3
42, 3eqtr4d 2501 . 2
5 iftrue 3947 . . 3
6 iffalse 3950 . . 3
75, 6eqtr4d 2501 . 2
84, 7pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  =wceq 1395  ifcif 3941 This theorem is referenced by:  suppsnop  6932  sadadd2lem2  14100  maducoeval2  19142  tmsxpsval2  21042  itg2uba  22150  lgsneg  23594  lgsdilem  23597  sgnneg  28479  itgaddnclem2  30074  ftc1anclem5  30094  bj-xpimasn  34512 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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