Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-imim21 Structured version   Visualization version   GIF version

Theorem bj-imim21 32766
Description: The propositional function (𝜒 → (. → 𝜃)) is decreasing. (Contributed by BJ, 19-Jul-2019.)
Assertion
Ref Expression
bj-imim21 ((𝜑𝜓) → ((𝜒 → (𝜓𝜃)) → (𝜒 → (𝜑𝜃))))

Proof of Theorem bj-imim21
StepHypRef Expression
1 imim1 83 . 2 ((𝜑𝜓) → ((𝜓𝜃) → (𝜑𝜃)))
21imim2d 57 1 ((𝜑𝜓) → ((𝜒 → (𝜓𝜃)) → (𝜒 → (𝜑𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  bj-imim21i  32767  bj-axc4  32808
  Copyright terms: Public domain W3C validator