Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  gen22 Structured version   Visualization version   GIF version

Theorem gen22 39372
Description: Virtual deduction generalizing rule for two quantifying variables and two virtual hypothesis. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen22.1 (   𝜑   ,   𝜓   ▶   𝜒   )
Assertion
Ref Expression
gen22 (   𝜑   ,   𝜓   ▶   𝑥𝑦𝜒   )
Distinct variable groups:   𝜑,𝑥   𝜑,𝑦   𝜓,𝑥   𝜓,𝑦
Allowed substitution hints:   𝜒(𝑥,𝑦)

Proof of Theorem gen22
StepHypRef Expression
1 gen22.1 . . . . 5 (   𝜑   ,   𝜓   ▶   𝜒   )
21dfvd2i 39326 . . . 4 (𝜑 → (𝜓𝜒))
32alrimdv 2009 . . 3 (𝜑 → (𝜓 → ∀𝑦𝜒))
43alrimdv 2009 . 2 (𝜑 → (𝜓 → ∀𝑥𝑦𝜒))
54dfvd2ir 39327 1 (   𝜑   ,   𝜓   ▶   𝑥𝑦𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wal 1629  (   wvd2 39318
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991
This theorem depends on definitions:  df-bi 197  df-an 383  df-vd2 39319
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator