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Theorem biimp3a 1251
Description: Infer implication from a logical equivalence. Similar to biimpa 284. (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 284 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
323impa 1110 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  nnawordex  6131  nn0addge1  8284  nn0addge2  8285  nn0sub2  8371  eluzp1p1  8593  uznn0sub  8599  iocssre  8922  icossre  8923  iccssre  8924  lincmb01cmp  8971  iccf1o  8972  fzosplitprm1  9191  subfzo0  9198  modfzo0difsn  9339
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