ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3anibar GIF version

Theorem 3anibar 1149
Description: Remove a hypothesis from the second member of a biimplication. (Contributed by FL, 22-Jul-2008.)
Hypothesis
Ref Expression
3anibar.1 ((𝜑𝜓𝜒) → (𝜃 ↔ (𝜒𝜏)))
Assertion
Ref Expression
3anibar ((𝜑𝜓𝜒) → (𝜃𝜏))

Proof of Theorem 3anibar
StepHypRef Expression
1 3anibar.1 . 2 ((𝜑𝜓𝜒) → (𝜃 ↔ (𝜒𝜏)))
2 simp3 983 . . 3 ((𝜑𝜓𝜒) → 𝜒)
32biantrurd 303 . 2 ((𝜑𝜓𝜒) → (𝜏 ↔ (𝜒𝜏)))
41, 3bitr4d 190 1 ((𝜑𝜓𝜒) → (𝜃𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104  w3a 962
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 964
This theorem is referenced by:  frecsuclem  6303  shftfibg  10604  neiint  12328
  Copyright terms: Public domain W3C validator