ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  biimp3ar GIF version

Theorem biimp3ar 1252
Description: Infer implication from a logical equivalence. Similar to biimpar 285. (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 368 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
323imp 1109 1 ((𝜑𝜓𝜃) → 𝜒)
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:  rmoi  2878  brelrng  4592  ssfzo12  9181  abssubge0  9928
  Copyright terms: Public domain W3C validator