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Theorem ee333 39667
 Description: e333 39902 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee333.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee333.2 (𝜑 → (𝜓 → (𝜒𝜏)))
ee333.3 (𝜑 → (𝜓 → (𝜒𝜂)))
ee333.4 (𝜃 → (𝜏 → (𝜂𝜁)))
Assertion
Ref Expression
ee333 (𝜑 → (𝜓 → (𝜒𝜁)))

Proof of Theorem ee333
StepHypRef Expression
1 ee333.1 . . . 4 (𝜑 → (𝜓 → (𝜒𝜃)))
213imp 1098 . . 3 ((𝜑𝜓𝜒) → 𝜃)
3 ee333.2 . . . 4 (𝜑 → (𝜓 → (𝜒𝜏)))
433imp 1098 . . 3 ((𝜑𝜓𝜒) → 𝜏)
5 ee333.3 . . . 4 (𝜑 → (𝜓 → (𝜒𝜂)))
653imp 1098 . . 3 ((𝜑𝜓𝜒) → 𝜂)
7 ee333.4 . . 3 (𝜃 → (𝜏 → (𝜂𝜁)))
82, 4, 6, 7syl3c 66 . 2 ((𝜑𝜓𝜒) → 𝜁)
983exp 1109 1 (𝜑 → (𝜓 → (𝜒𝜁)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1071 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  df-3an 1073 This theorem is referenced by:  ee323  39668  ee123  39932
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