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

Theorem iba 295
Description: Introduction of antecedent as conjunct. Theorem *4.73 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-Mar-1994.) (Revised by NM, 24-Mar-2013.)
Assertion
Ref Expression
iba (𝜑 → (𝜓 ↔ (𝜓𝜑)))

Proof of Theorem iba
StepHypRef Expression
1 pm3.21 261 . 2 (𝜑 → (𝜓 → (𝜓𝜑)))
2 simpl 108 . 2 ((𝜓𝜑) → 𝜓)
31, 2impbid1 141 1 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  biantru  297  biantrud  299  ancrb  316  rbaibd  874  dedlem0a  917  fvopab6  5435  fressnfv  5523  tpostpos  6067  nnmword  6317  unfiexmid  6708  ltmpig  6995  sup3exmid  8515  xrmaxiflemcom  10808
  Copyright terms: Public domain W3C validator