MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.36 Structured version   Visualization version   GIF version

Theorem pm2.36 883
Description: Theorem *2.36 of [WhiteheadRussell] p. 105. (Contributed by NM, 6-Mar-2008.)
Assertion
Ref Expression
pm2.36 ((𝜓𝜒) → ((𝜑𝜓) → (𝜒𝜑)))

Proof of Theorem pm2.36
StepHypRef Expression
1 pm1.4 399 . 2 ((𝜑𝜓) → (𝜓𝜑))
2 pm2.38 882 . 2 ((𝜓𝜒) → ((𝜓𝜑) → (𝜒𝜑)))
31, 2syl5 33 1 ((𝜓𝜒) → ((𝜑𝜓) → (𝜒𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381
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 195  df-or 383  df-an 384
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator