Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  gen21 Structured version   Visualization version   GIF version

Theorem gen21 41245
Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 41245 is alrimdv 1931 with virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen21.1 (   𝜑   ,   𝜓   ▶   𝜒   )
Assertion
Ref Expression
gen21 (   𝜑   ,   𝜓   ▶   𝑥𝜒   )
Distinct variable groups:   𝜑,𝑥   𝜓,𝑥
Allowed substitution hint:   𝜒(𝑥)

Proof of Theorem gen21
StepHypRef Expression
1 gen21.1 . . . 4 (   𝜑   ,   𝜓   ▶   𝜒   )
21dfvd2i 41211 . . 3 (𝜑 → (𝜓𝜒))
32alrimdv 1931 . 2 (𝜑 → (𝜓 → ∀𝑥𝜒))
43dfvd2ir 41212 1 (   𝜑   ,   𝜓   ▶   𝑥𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wal 1536  (   wvd2 41203
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912
This theorem depends on definitions:  df-bi 210  df-an 400  df-vd2 41204
This theorem is referenced by:  truniALTVD  41504  trintALTVD  41506  onfrALTlem2VD  41515
  Copyright terms: Public domain W3C validator