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Theorem gen21 39369
Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 39369 is alrimdv 2009 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 39326 . . 3 (𝜑 → (𝜓𝜒))
32alrimdv 2009 . 2 (𝜑 → (𝜓 → ∀𝑥𝜒))
43dfvd2ir 39327 1 (   𝜑   ,   𝜓   ▶   𝑥𝜒   )
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:  truniALTVD  39636  trintALTVD  39638  onfrALTlem2VD  39647
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