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Theorem gen21 44332
Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 44332 is alrimdv 1925 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 44298 . . 3 (𝜑 → (𝜓𝜒))
32alrimdv 1925 . 2 (𝜑 → (𝜓 → ∀𝑥𝜒))
43dfvd2ir 44299 1 (   𝜑   ,   𝜓   ▶   𝑥𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wal 1532  (   wvd2 44290
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906
This theorem depends on definitions:  df-bi 206  df-an 395  df-vd2 44291
This theorem is referenced by:  truniALTVD  44591  trintALTVD  44593  onfrALTlem2VD  44602
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