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Theorem biimp3ar 1307
Description: Infer implication from a logical equivalence. Similar to biimpar 293. (Contributed by NM, 2-Jan-2009.)
Hypothesis
Ref Expression
biimp3a.1 ((𝜑𝜓) → (𝜒𝜃))
Assertion
Ref Expression
biimp3ar ((𝜑𝜓𝜃) → 𝜒)

Proof of Theorem biimp3ar
StepHypRef Expression
1 biimp3a.1 . . 3 ((𝜑𝜓) → (𝜒𝜃))
21exbiri 377 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
323imp 1158 1 ((𝜑𝜓𝜃) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104  w3a 945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by:  rmoi  2972  brelrng  4738  ssfzo12  9952  abssubge0  10825  qredeu  11685  basgen2  12156
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