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Theorem gen21 38361
Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 38361 is alrimdv 1854 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 38318 . . 3 (𝜑 → (𝜓𝜒))
32alrimdv 1854 . 2 (𝜑 → (𝜓 → ∀𝑥𝜒))
43dfvd2ir 38319 1 (   𝜑   ,   𝜓   ▶   𝑥𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wal 1478  (   wvd2 38310
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836
This theorem depends on definitions:  df-bi 197  df-an 386  df-vd2 38311
This theorem is referenced by:  truniALTVD  38632  trintALTVD  38634  onfrALTlem2VD  38643
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