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Theorem biimp3a 1281
Description: Infer implication from a logical equivalence. Similar to biimpa 290. (Contributed by NM, 4-Sep-2005.)
Hypothesis
Ref Expression
biimp3a.1 ((𝜑𝜓) → (𝜒𝜃))
Assertion
Ref Expression
biimp3a ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem biimp3a
StepHypRef Expression
1 biimp3a.1 . . 3 ((𝜑𝜓) → (𝜒𝜃))
21biimpa 290 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
323impa 1138 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103  w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by:  nnawordex  6285  div2subap  8300  nn0addge1  8717  nn0addge2  8718  nn0sub2  8818  eluzp1p1  9042  uznn0sub  9048  iocssre  9369  icossre  9370  iccssre  9371  lincmb01cmp  9418  iccf1o  9419  fzosplitprm1  9641  subfzo0  9649  modfzo0difsn  9798  efltim  10984  fldivndvdslt  11209  hashgcdlem  11477
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