MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imp55 Structured version   Visualization version   GIF version

Theorem imp55 433
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp55 (((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) ∧ 𝜏) → 𝜂)

Proof of Theorem imp55
StepHypRef Expression
1 imp5.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21imp4a 413 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → (𝜏𝜂))))
32imp42 417 1 (((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) ∧ 𝜏) → 𝜂)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 198  df-an 385
This theorem is referenced by:  alexsubALTlem4  22136
  Copyright terms: Public domain W3C validator