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Theorem biimp3a 1235
Description: Infer implication from a logical equivalence. Similar to biimpa 280. (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 280 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
323impa 1099 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  wb 98  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  nnawordex  6088  nn0addge1  8200  nn0addge2  8201  nn0sub2  8286  eluzp1p1  8470  uznn0sub  8476  iocssre  8789  icossre  8790  iccssre  8791  lincmb01cmp  8838  iccf1o  8839  fzosplitprm1  9057
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