Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  naim2i Structured version   Visualization version   GIF version

Theorem naim2i 33728
Description: Constructor rule for . (Contributed by Anthony Hart, 2-Sep-2011.)
Hypotheses
Ref Expression
naim2i.1 (𝜑𝜓)
naim2i.2 (𝜒𝜓)
Assertion
Ref Expression
naim2i (𝜒𝜑)

Proof of Theorem naim2i
StepHypRef Expression
1 naim2i.1 . 2 (𝜑𝜓)
2 naim2i.2 . 2 (𝜒𝜓)
3 naim2 33726 . 2 ((𝜑𝜓) → ((𝜒𝜓) → (𝜒𝜑)))
41, 2, 3mp2 9 1 (𝜒𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnan 1477
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 209  df-an 399  df-or 844  df-nan 1478
This theorem is referenced by:  naim12i  33729
  Copyright terms: Public domain W3C validator