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Theorem int2 39148
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 39148 is ex 449. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
int2.1 (   (   𝜑   ,   𝜓   )   ▶   𝜒   )
Assertion
Ref Expression
int2 (   𝜑   ▶   (𝜓𝜒)   )

Proof of Theorem int2
StepHypRef Expression
1 int2.1 . . . 4 (   (   𝜑   ,   𝜓   )   ▶   𝜒   )
21dfvd2ani 39116 . . 3 ((𝜑𝜓) → 𝜒)
32ex 449 . 2 (𝜑 → (𝜓𝜒))
43dfvd1ir 39106 1 (   𝜑   ▶   (𝜓𝜒)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39102  (   wvhc2 39113
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 39103  df-vhc2 39114
This theorem is referenced by:  sspwimpVD  39469  sspwimpcfVD  39471  suctrALTcfVD  39473
  Copyright terms: Public domain W3C validator