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Theorem dfvd2 39314
Description: Definition of a 2-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd2 ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓𝜒)))

Proof of Theorem dfvd2
StepHypRef Expression
1 df-vd2 39313 . 2 ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))
2 impexp 437 . 2 (((𝜑𝜓) → 𝜒) ↔ (𝜑 → (𝜓𝜒)))
31, 2bitri 264 1 ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 382  (   wvd2 39312
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 383  df-vd2 39313
This theorem is referenced by:  dfvd2i  39320  dfvd2ir  39321  dfvd2imp  39347  dfvd2impr  39348
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