NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  3anibar GIF version

Theorem 3anibar 1123
Description: Remove a hypothesis from the second member of a biimplication. (Contributed by FL, 22-Jul-2008.)
Hypothesis
Ref Expression
3anibar.1 ((φ ψ χ) → (θ ↔ (χ τ)))
Assertion
Ref Expression
3anibar ((φ ψ χ) → (θτ))

Proof of Theorem 3anibar
StepHypRef Expression
1 3anibar.1 . 2 ((φ ψ χ) → (θ ↔ (χ τ)))
2 simp3 957 . . 3 ((φ ψ χ) → χ)
32biantrurd 494 . 2 ((φ ψ χ) → (τ ↔ (χ τ)))
41, 3bitr4d 247 1 ((φ ψ χ) → (θτ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator