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Theorem ifeqor 3936
 Description: The possible values of a conditional operator. (Contributed by NM, 17-Jun-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
ifeqor

Proof of Theorem ifeqor
StepHypRef Expression
1 iftrue 3900 . . . 4
21con3i 135 . . 3
3 iffalse 3902 . . 3
42, 3syl 16 . 2
54orri 376 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 368   wceq 1370  cif 3894 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-if 3895 This theorem is referenced by:  ifpr  4027  rabrsn  4048  muval2  22600  axlowdimlem15  23349
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