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Theorem in2an 39150
Description: The virtual deduction introduction rule converting the second conjunct of the second virtual hypothesis into the antecedent of the conclusion. expd 451 is the non-virtual deduction form of in2an 39150. (Contributed by Alan Sare, 30-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
in2an.1 (   𝜑   ,   (𝜓𝜒)   ▶   𝜃   )
Assertion
Ref Expression
in2an (   𝜑   ,   𝜓   ▶   (𝜒𝜃)   )

Proof of Theorem in2an
StepHypRef Expression
1 in2an.1 . . . 4 (   𝜑   ,   (𝜓𝜒)   ▶   𝜃   )
21dfvd2i 39118 . . 3 (𝜑 → ((𝜓𝜒) → 𝜃))
32expd 451 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
43dfvd2ir 39119 1 (   𝜑   ,   𝜓   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  (   wvd2 39110
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-vd2 39111
This theorem is referenced by:  onfrALTVD  39441
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