ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simplbi2 GIF version

Theorem simplbi2 377
Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011.)
Hypothesis
Ref Expression
pm3.26bi2.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
simplbi2 (𝜓 → (𝜒𝜑))

Proof of Theorem simplbi2
StepHypRef Expression
1 pm3.26bi2.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21biimpri 131 . 2 ((𝜓𝜒) → 𝜑)
32ex 113 1 (𝜓 → (𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.62dc  891  pm5.63dc  892  simplbi2com  1378  reuss2  3279  elni2  6871  elfz0ubfz0  9532  elfzmlbp  9539  fzo1fzo0n0  9590  elfzo0z  9591  fzofzim  9595  elfzodifsumelfzo  9608  dfgcd2  11277  ialgcvga  11307
  Copyright terms: Public domain W3C validator