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

Theorem simplbda 382
Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007.)
Hypothesis
Ref Expression
pm3.26bda.1 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
Assertion
Ref Expression
simplbda ((𝜑𝜓) → 𝜃)

Proof of Theorem simplbda
StepHypRef Expression
1 pm3.26bda.1 . . 3 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
21biimpa 294 . 2 ((𝜑𝜓) → (𝜒𝜃))
32simprd 113 1 ((𝜑𝜓) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  tgcl  12270  cldopn  12313  cncnp  12436  blgt0  12608  xblss2ps  12610  xblss2  12611  mopni  12688  metrest  12712  dvcl  12858  dvcnp2cntop  12869
  Copyright terms: Public domain W3C validator