MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imim3i Structured version   Visualization version   GIF version

Theorem imim3i 64
Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006.)
Hypothesis
Ref Expression
imim3i.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
imim3i ((𝜃𝜑) → ((𝜃𝜓) → (𝜃𝜒)))

Proof of Theorem imim3i
StepHypRef Expression
1 imim3i.1 . . 3 (𝜑 → (𝜓𝜒))
21imim2i 16 . 2 ((𝜃𝜑) → (𝜃 → (𝜓𝜒)))
32a2d 29 1 ((𝜃𝜑) → ((𝜃𝜓) → (𝜃𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  pm2.83  84  pm5.74  259  pm3.43i  472  ral2imi  2943  ceqsalt  3218  bj-bi3ant  32269  bj-ceqsalt0  32573  bj-ceqsalt1  32574  pm10.57  38091  ee33  38248
  Copyright terms: Public domain W3C validator