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Theorem e02an 41324
 Description: Conjunction form of e02 41323. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e02an.1 𝜑
e02an.2 (   𝜓   ,   𝜒   ▶   𝜃   )
e02an.3 ((𝜑𝜃) → 𝜏)
Assertion
Ref Expression
e02an (   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e02an
StepHypRef Expression
1 e02an.1 . 2 𝜑
2 e02an.2 . 2 (   𝜓   ,   𝜒   ▶   𝜃   )
3 e02an.3 . . 3 ((𝜑𝜃) → 𝜏)
43ex 416 . 2 (𝜑 → (𝜃𝜏))
51, 2, 4e02 41323 1 (   𝜓   ,   𝜒   ▶   𝜏   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399  (   wvd2 41203 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  df-vd2 41204 This theorem is referenced by: (None)
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