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Theorem ifnefalse 3490
 Description: When values are unequal, but an "if" condition checks if they are equal, then the "false" branch results. This is a simple utility to provide a slight shortening and simplification of proofs versus applying iffalse 3487 directly in this case. (Contributed by David A. Wheeler, 15-May-2015.)
Assertion
Ref Expression
ifnefalse

Proof of Theorem ifnefalse
StepHypRef Expression
1 df-ne 2310 . 2
2 iffalse 3487 . 2
31, 2sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1332   wne 2309  cif 3479 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-ne 2310  df-if 3480 This theorem is referenced by:  xnegmnf  9643  rexneg  9644  xaddpnf1  9660  xaddpnf2  9661  xaddmnf1  9662  xaddmnf2  9663  mnfaddpnf  9665  rexadd  9666  fztpval  9895
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