MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  bitr3 Structured version   Visualization version   GIF version

Theorem bitr3 341
Description: Closed nested implication form of bitr3i 266. Derived automatically from bitr3VD 39500. (Contributed by Alan Sare, 31-Dec-2011.)
Assertion
Ref Expression
bitr3 ((𝜑𝜓) → ((𝜑𝜒) → (𝜓𝜒)))

Proof of Theorem bitr3
StepHypRef Expression
1 bibi1 340 . 2 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
21biimpd 219 1 ((𝜑𝜓) → ((𝜑𝜒) → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197
This theorem is referenced by:  sumodd  15234  3orbi123VD  39501  sbc3orgVD  39502  trsbcVD  39529  csbrngVD  39548  e2ebindVD  39564  e2ebindALT  39581
  Copyright terms: Public domain W3C validator