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Theorem e21an 39478
 Description: Conjunction form of e21 39477. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e21an.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e21an.2 (   𝜑   ▶   𝜃   )
e21an.3 ((𝜒𝜃) → 𝜏)
Assertion
Ref Expression
e21an (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e21an
StepHypRef Expression
1 e21an.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e21an.2 . 2 (   𝜑   ▶   𝜃   )
3 e21an.3 . . 3 ((𝜒𝜃) → 𝜏)
43ex 449 . 2 (𝜒 → (𝜃𝜏))
51, 2, 4e21 39477 1 (   𝜑   ,   𝜓   ▶   𝜏   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  (   wvd1 39305  (   wvd2 39313 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 197  df-an 385  df-vd1 39306  df-vd2 39314 This theorem is referenced by: (None)
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