Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  int3 Structured version   Visualization version   GIF version

Theorem int3 39154
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 39154 is 3expia 1286. (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 39128 . . 3 ((𝜑𝜓𝜒) → 𝜃)
323expia 1286 . 2 ((𝜑𝜓) → (𝜒𝜃))
43dfvd2anir 39117 1 (   (   𝜑   ,   𝜓   )   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39102  (   wvhc2 39113  (   wvhc3 39121
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-3an 1056  df-vd1 39103  df-vhc2 39114  df-vhc3 39122
This theorem is referenced by:  suctrALTcfVD  39473
  Copyright terms: Public domain W3C validator