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Theorem ee13 39027
Description: e13 39292 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee13.1 (𝜑𝜓)
ee13.2 (𝜑 → (𝜒 → (𝜃𝜏)))
ee13.3 (𝜓 → (𝜏𝜂))
Assertion
Ref Expression
ee13 (𝜑 → (𝜒 → (𝜃𝜂)))

Proof of Theorem ee13
StepHypRef Expression
1 ee13.2 . 2 (𝜑 → (𝜒 → (𝜃𝜏)))
2 ee13.1 . . 3 (𝜑𝜓)
3 ee13.3 . . 3 (𝜓 → (𝜏𝜂))
42, 3syl 17 . 2 (𝜑 → (𝜏𝜂))
51, 4syl6d 75 1 (𝜑 → (𝜒 → (𝜃𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  sbcim2g  39065  ee13an  39294
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