NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  bi2.04 GIF version

Theorem bi2.04 350
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 76 . 2 ((φ → (ψχ)) → (ψ → (φχ)))
2 pm2.04 76 . 2 ((ψ → (φχ)) → (φ → (ψχ)))
31, 2impbii 180 1 ((φ → (ψχ)) ↔ (ψ → (φχ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  imim21b  356  pm4.87  567  imimorb  847  ax12bOLD  1690  sbcom  2089  sbcom2  2114  r19.21t  2699  reu8  3032  ra5  3130  unissb  3921  fun11  5159  spacind  6285
  Copyright terms: Public domain W3C validator