ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  bi2.04 GIF version

Theorem bi2.04 247
Description: Logical equivalence of commuted antecedents. Part of Theorem *4.87 of [WhiteheadRussell] p. 122. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
bi2.04 ((𝜑 → (𝜓𝜒)) ↔ (𝜓 → (𝜑𝜒)))

Proof of Theorem bi2.04
StepHypRef Expression
1 pm2.04 82 . 2 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
2 pm2.04 82 . 2 ((𝜓 → (𝜑𝜒)) → (𝜑 → (𝜓𝜒)))
31, 2impbii 125 1 ((𝜑 → (𝜓𝜒)) ↔ (𝜓 → (𝜑𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  imim21b  251  pm4.87  547  imimorbdc  886  sbcom2v  1972  mor  2055  r19.21t  2539  reu8  2918  ra5  3035  unissb  3814  reusv3  4433  zfregfr  4546  tfi  4554  fun11  5250  prime  9282  raluz2  9509  isprm3  12039  isprm4  12040  bj-inf2vnlem2  13715
  Copyright terms: Public domain W3C validator