MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.33 Structured version   Visualization version   GIF version

Theorem pm3.33 606
Description: Theorem *3.33 (Syll) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm3.33 (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))

Proof of Theorem pm3.33
StepHypRef Expression
1 imim1 80 . 2 ((𝜑𝜓) → ((𝜓𝜒) → (𝜑𝜒)))
21imp 443 1 (((𝜑𝜓) ∧ (𝜓𝜒)) → (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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-an 384
This theorem is referenced by:  alsyl  1809  ucncn  21837  bnj1023  29907  bnj907  30091  2sb5ndALT  37989
  Copyright terms: Public domain W3C validator