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

Theorem abai 494
Description: Introduce one conjunct as an antecedent to the other. "abai" stands for "and, biconditional, and, implication". (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)
Assertion
Ref Expression
abai ((φ ψ) ↔ (φ (φψ)))

Proof of Theorem abai
StepHypRef Expression
1 biimt 230 . 2 (φ → (ψ ↔ (φψ)))
21pm5.32i 427 1 ((φ ψ) ↔ (φ (φψ)))
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:  eu2  1941
  Copyright terms: Public domain W3C validator