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Theorem sylnib 666
 Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by Wolf Lammen, 16-Dec-2013.)
Hypotheses
Ref Expression
sylnib.1
sylnib.2
Assertion
Ref Expression
sylnib

Proof of Theorem sylnib
StepHypRef Expression
1 sylnib.1 . 2
2 sylnib.2 . . 3
32a1i 9 . 2
41, 3mtbid 662 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104 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-in1 604  ax-in2 605 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  sylnibr  667  neqcomd  2145  inssdif0im  3436  undifexmid  4126  ordtriexmidlem2  4445  dmsn0el  5018  fidifsnen  6774  ctssdccl  7009  onntri35  7111  onntri45  7114  ltpopr  7450  caucvgprprlemnbj  7548  xrlttri3  9636  fzneuz  9935  iseqf1olemqcl  10313  iseqf1olemnab  10315  iseqf1olemab  10316  exp3val  10349  pwle2  13398
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