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

Theorem iba 284
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 ↔ (ψ φ)))

Proof of Theorem iba
StepHypRef Expression
1 pm3.21 251 . 2 (φ → (ψ → (ψ φ)))
2 simpl 102 . 2 ((ψ φ) → ψ)
31, 2impbid1 130 1 (φ → (ψ ↔ (ψ φ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  biantru  286  biantrud  288  ancrb  305  rbaibd  832  dedlem0a  874  fvopab6  5207  fressnfv  5293  tpostpos  5820  nnmword  6027  ltmpig  6323
  Copyright terms: Public domain W3C validator