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Theorem e22an 41365
Description: Conjunction form of e22 41364. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e22an.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e22an.2 (   𝜑   ,   𝜓   ▶   𝜃   )
e22an.3 ((𝜒𝜃) → 𝜏)
Assertion
Ref Expression
e22an (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e22an
StepHypRef Expression
1 e22an.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e22an.2 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
3 e22an.3 . . 3 ((𝜒𝜃) → 𝜏)
43ex 416 . 2 (𝜒 → (𝜃𝜏))
51, 2, 4e22 41364 1 (   𝜑   ,   𝜓   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  (   wvd2 41270
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 41271
This theorem is referenced by: (None)
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