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Theorem int3 40808
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 40808 is 3expia 1115. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
int3.1 (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )
Assertion
Ref Expression
int3 (   (   𝜑   ,   𝜓   )   ▶   (𝜒𝜃)   )

Proof of Theorem int3
StepHypRef Expression
1 int3.1 . . . 4 (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )
21dfvd3ani 40791 . . 3 ((𝜑𝜓𝜒) → 𝜃)
323expia 1115 . 2 ((𝜑𝜓) → (𝜒𝜃))
43dfvd2anir 40780 1 (   (   𝜑   ,   𝜓   )   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 40765  (   wvhc2 40776  (   wvhc3 40784
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 208  df-an 397  df-3an 1083  df-vd1 40766  df-vhc2 40777  df-vhc3 40785
This theorem is referenced by:  suctrALTcfVD  41119
  Copyright terms: Public domain W3C validator