MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ibd Structured version   Visualization version   GIF version

Theorem ibd 256
Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. Deduction associated with ibi 254. (Contributed by NM, 26-Jun-2004.)
Hypothesis
Ref Expression
ibd.1 (𝜑 → (𝜓 → (𝜓𝜒)))
Assertion
Ref Expression
ibd (𝜑 → (𝜓𝜒))

Proof of Theorem ibd
StepHypRef Expression
1 ibd.1 . 2 (𝜑 → (𝜓 → (𝜓𝜒)))
2 biimp 203 . 2 ((𝜓𝜒) → (𝜓𝜒))
31, 2syli 38 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194
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 195
This theorem is referenced by:  sssn  4295  unblem2  8075  atcv0eq  28415  atcv1  28416  atomli  28418  atcvatlem  28421  ibdr  32941
  Copyright terms: Public domain W3C validator