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Theorem ee03an 38790
Description: Conjunction form of ee03 38788. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee03an.1 𝜑
ee03an.2 (𝜓 → (𝜒 → (𝜃𝜏)))
ee03an.3 ((𝜑𝜏) → 𝜂)
Assertion
Ref Expression
ee03an (𝜓 → (𝜒 → (𝜃𝜂)))

Proof of Theorem ee03an
StepHypRef Expression
1 ee03an.1 . 2 𝜑
2 ee03an.2 . 2 (𝜓 → (𝜒 → (𝜃𝜏)))
3 ee03an.3 . . 3 ((𝜑𝜏) → 𝜂)
43ex 450 . 2 (𝜑 → (𝜏𝜂))
51, 2, 4ee03 38788 1 (𝜓 → (𝜒 → (𝜃𝜂)))
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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