ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm4.77 GIF version

Theorem pm4.77 723
Description: Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.77 (((𝜓𝜑) ∧ (𝜒𝜑)) ↔ ((𝜓𝜒) → 𝜑))

Proof of Theorem pm4.77
StepHypRef Expression
1 jaob 641 . 2 (((𝜓𝜒) → 𝜑) ↔ ((𝜓𝜑) ∧ (𝜒𝜑)))
21bicomi 127 1 (((𝜓𝜑) ∧ (𝜒𝜑)) ↔ ((𝜓𝜒) → 𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator