MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.42 Structured version   Visualization version   GIF version

Theorem pm3.42 497
Description: Theorem *3.42 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm3.42 ((𝜓𝜒) → ((𝜑𝜓) → 𝜒))

Proof of Theorem pm3.42
StepHypRef Expression
1 simpr 488 . 2 ((𝜑𝜓) → 𝜓)
21imim1i 63 1 ((𝜓𝜒) → ((𝜑𝜓) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399
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 210  df-an 400
This theorem is referenced by:  bnj1101  32064  islinindfis  44680
  Copyright terms: Public domain W3C validator