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Theorem ee33an 39790
 Description: e33an 39789 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee33an.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee33an.2 (𝜑 → (𝜓 → (𝜒𝜏)))
ee33an.3 ((𝜃𝜏) → 𝜂)
Assertion
Ref Expression
ee33an (𝜑 → (𝜓 → (𝜒𝜂)))

Proof of Theorem ee33an
StepHypRef Expression
1 ee33an.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 ee33an.2 . 2 (𝜑 → (𝜓 → (𝜒𝜏)))
3 ee33an.3 . . 3 ((𝜃𝜏) → 𝜂)
43ex 403 . 2 (𝜃 → (𝜏𝜂))
51, 2, 4ee33 39565 1 (𝜑 → (𝜓 → (𝜒𝜂)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 386 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 199  df-an 387 This theorem is referenced by:  ee31an  39808  ee23an  39811  ee32an  39815
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