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Theorem ee30an 42069
Description: Conjunction form of ee30 42067. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee30an.1 (𝜑 → (𝜓 → (𝜒𝜃)))
ee30an.2 𝜏
ee30an.3 ((𝜃𝜏) → 𝜂)
Assertion
Ref Expression
ee30an (𝜑 → (𝜓 → (𝜒𝜂)))

Proof of Theorem ee30an
StepHypRef Expression
1 ee30an.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 ee30an.2 . 2 𝜏
3 ee30an.3 . . 3 ((𝜃𝜏) → 𝜂)
43ex 416 . 2 (𝜃 → (𝜏𝜂))
51, 2, 4ee30 42067 1 (𝜑 → (𝜓 → (𝜒𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399
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)
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