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Theorem ee102 41371
Description: e102 41370 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee102.1 (𝜑𝜓)
ee102.2 𝜒
ee102.3 (𝜑 → (𝜃𝜏))
ee102.4 (𝜓 → (𝜒 → (𝜏𝜂)))
Assertion
Ref Expression
ee102 (𝜑 → (𝜃𝜂))

Proof of Theorem ee102
StepHypRef Expression
1 ee102.1 . . 3 (𝜑𝜓)
21a1d 25 . 2 (𝜑 → (𝜃𝜓))
3 ee102.2 . . . 4 𝜒
43a1i 11 . . 3 (𝜃𝜒)
54a1i 11 . 2 (𝜑 → (𝜃𝜒))
6 ee102.3 . 2 (𝜑 → (𝜃𝜏))
7 ee102.4 . 2 (𝜓 → (𝜒 → (𝜏𝜂)))
82, 5, 6, 7ee222 41203 1 (𝜑 → (𝜃𝜂))
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