Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ee32 Structured version   Visualization version   GIF version

Theorem ee32 38465
Description: e32 38464 without virtual deductions. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee32.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee32.2 (𝜑 → (𝜓𝜏))
ee32.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
ee32 (𝜑 → (𝜓 → (𝜒𝜂)))

Proof of Theorem ee32
StepHypRef Expression
1 ee32.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 ee32.2 . . 3 (𝜑 → (𝜓𝜏))
32a1dd 50 . 2 (𝜑 → (𝜓 → (𝜒𝜏)))
4 ee32.3 . 2 (𝜃 → (𝜏𝜂))
51, 3, 4ee33 38206 1 (𝜑 → (𝜓 → (𝜒𝜂)))
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: (None)
  Copyright terms: Public domain W3C validator