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Theorem ee13an 39735
Description: e13an 39734 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee13an.1 (𝜑𝜓)
ee13an.2 (𝜑 → (𝜒 → (𝜃𝜏)))
ee13an.3 ((𝜓𝜏) → 𝜂)
Assertion
Ref Expression
ee13an (𝜑 → (𝜒 → (𝜃𝜂)))

Proof of Theorem ee13an
StepHypRef Expression
1 ee13an.1 . 2 (𝜑𝜓)
2 ee13an.2 . 2 (𝜑 → (𝜒 → (𝜃𝜏)))
3 ee13an.3 . . 3 ((𝜓𝜏) → 𝜂)
43ex 402 . 2 (𝜓 → (𝜏𝜂))
51, 2, 4ee13 39479 1 (𝜑 → (𝜒 → (𝜃𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385
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 386
This theorem is referenced by: (None)
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