Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ee210 Structured version   Visualization version   GIF version

Theorem ee210 41286
Description: e210 41285 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee210.1 (𝜑 → (𝜓𝜒))
ee210.2 (𝜑𝜃)
ee210.3 𝜏
ee210.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee210 (𝜑 → (𝜓𝜂))

Proof of Theorem ee210
StepHypRef Expression
1 ee210.1 . 2 (𝜑 → (𝜓𝜒))
2 ee210.2 . . 3 (𝜑𝜃)
32a1d 25 . 2 (𝜑 → (𝜓𝜃))
4 ee210.3 . . . 4 𝜏
54a1i 11 . . 3 (𝜓𝜏)
65a1i 11 . 2 (𝜑 → (𝜓𝜏))
7 ee210.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
81, 3, 6, 7ee222 41128 1 (𝜑 → (𝜓𝜂))
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  ax-3 8
This theorem depends on definitions:  df-bi 210  df-an 400
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator