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Theorem e12an 39613
 Description: Conjunction form of e12 39612 (see syl6an 674). (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e12an.1 (   𝜑   ▶   𝜓   )
e12an.2 (   𝜑   ,   𝜒   ▶   𝜃   )
e12an.3 ((𝜓𝜃) → 𝜏)
Assertion
Ref Expression
e12an (   𝜑   ,   𝜒   ▶   𝜏   )

Proof of Theorem e12an
StepHypRef Expression
1 e12an.1 . 2 (   𝜑   ▶   𝜓   )
2 e12an.2 . 2 (   𝜑   ,   𝜒   ▶   𝜃   )
3 e12an.3 . . 3 ((𝜓𝜃) → 𝜏)
43ex 401 . 2 (𝜓 → (𝜃𝜏))
51, 2, 4e12 39612 1 (   𝜑   ,   𝜒   ▶   𝜏   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 384  (   wvd1 39447  (   wvd2 39455 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 198  df-an 385  df-vd1 39448  df-vd2 39456 This theorem is referenced by:  sstrALT2VD  39722
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