Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  vd02 Structured version   Visualization version   GIF version

Theorem vd02 39140
Description: Two virtual hypotheses virtually infer a theorem. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd02.1 𝜑
Assertion
Ref Expression
vd02 (   𝜓   ,   𝜒   ▶   𝜑   )

Proof of Theorem vd02
StepHypRef Expression
1 vd02.1 . . . 4 𝜑
21a1i 11 . . 3 (𝜒𝜑)
32a1i 11 . 2 (𝜓 → (𝜒𝜑))
43dfvd2ir 39119 1 (   𝜓   ,   𝜒   ▶   𝜑   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   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:  e220  39179  e202  39181  e022  39183  e002  39185  e020  39187  e200  39189  e02  39239  e20  39271
  Copyright terms: Public domain W3C validator