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Theorem ee201 41288
Description: e201 41287 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee201.1 (𝜑 → (𝜓𝜒))
ee201.2 𝜃
ee201.3 (𝜑𝜏)
ee201.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee201 (𝜑 → (𝜓𝜂))

Proof of Theorem ee201
StepHypRef Expression
1 ee201.1 . 2 (𝜑 → (𝜓𝜒))
2 ee201.2 . . . 4 𝜃
32a1i 11 . . 3 (𝜓𝜃)
43a1i 11 . 2 (𝜑 → (𝜓𝜃))
5 ee201.3 . . 3 (𝜑𝜏)
65a1d 25 . 2 (𝜑 → (𝜓𝜏))
7 ee201.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
81, 4, 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