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Theorem ee32an 38456
Description: e33an 38430 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee32an.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee32an.2 (𝜑 → (𝜓𝜏))
ee32an.3 ((𝜃𝜏) → 𝜂)
Assertion
Ref Expression
ee32an (𝜑 → (𝜓 → (𝜒𝜂)))

Proof of Theorem ee32an
StepHypRef Expression
1 ee32an.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 ee32an.2 . . 3 (𝜑 → (𝜓𝜏))
32a1dd 50 . 2 (𝜑 → (𝜓 → (𝜒𝜏)))
4 ee32an.3 . 2 ((𝜃𝜏) → 𝜂)
51, 3, 4ee33an 38431 1 (𝜑 → (𝜓 → (𝜒𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 197  df-an 386
This theorem is referenced by: (None)
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