Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  vd13 Structured version   Visualization version   GIF version

Theorem vd13 40925
Description: A virtual deduction with 1 virtual hypothesis virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same virtual hypothesis and a two additional hypotheses. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd13.1 (   𝜑   ▶   𝜓   )
Assertion
Ref Expression
vd13 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜓   )

Proof of Theorem vd13
StepHypRef Expression
1 vd13.1 . . . . 5 (   𝜑   ▶   𝜓   )
21in1 40895 . . . 4 (𝜑𝜓)
32a1d 25 . . 3 (𝜑 → (𝜒𝜓))
43a1dd 50 . 2 (𝜑 → (𝜒 → (𝜃𝜓)))
54dfvd3ir 40917 1 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  (   wvd1 40893  (   wvd3 40911
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 209  df-an 399  df-3an 1084  df-vd1 40894  df-vd3 40914
This theorem is referenced by:  e13  41072  e31  41075  e123  41086
  Copyright terms: Public domain W3C validator