Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ee22an Structured version   Visualization version   GIF version

Theorem ee22an 39317
Description: e22an 39316 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee22an.1 (𝜑 → (𝜓𝜒))
ee22an.2 (𝜑 → (𝜓𝜃))
ee22an.3 ((𝜒𝜃) → 𝜏)
Assertion
Ref Expression
ee22an (𝜑 → (𝜓𝜏))

Proof of Theorem ee22an
StepHypRef Expression
1 ee22an.1 . 2 (𝜑 → (𝜓𝜒))
2 ee22an.2 . 2 (𝜑 → (𝜓𝜃))
3 ee22an.3 . . 3 ((𝜒𝜃) → 𝜏)
43ex 449 . 2 (𝜒 → (𝜃𝜏))
51, 2, 4syl6c 70 1 (𝜑 → (𝜓𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 197  df-an 385
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator