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

Theorem anclb 317
Description: Conjoin antecedent to left of consequent. Theorem *4.7 of [WhiteheadRussell] p. 120. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
anclb ((𝜑𝜓) ↔ (𝜑 → (𝜑𝜓)))

Proof of Theorem anclb
StepHypRef Expression
1 ibar 299 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21pm5.74i 179 1 ((𝜑𝜓) ↔ (𝜑 → (𝜑𝜓)))
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  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm4.71  386  mo3h  2030
  Copyright terms: Public domain W3C validator