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Theorem ee02an 41325
Description: e02an 41324 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee02an.1 𝜑
ee02an.2 (𝜓 → (𝜒𝜃))
ee02an.3 ((𝜑𝜃) → 𝜏)
Assertion
Ref Expression
ee02an (𝜓 → (𝜒𝜏))

Proof of Theorem ee02an
StepHypRef Expression
1 ee02an.1 . 2 𝜑
2 ee02an.2 . 2 (𝜓 → (𝜒𝜃))
3 ee02an.3 . . 3 ((𝜑𝜃) → 𝜏)
43ex 416 . 2 (𝜑 → (𝜃𝜏))
51, 2, 4mpsylsyld 69 1 (𝜓 → (𝜒𝜏))
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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