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Theorem gen12 39600
Description: Virtual deduction generalizing rule for two quantifying variables and one virtual hypothesis. gen12 39600 is alrimivv 2024 with virtual deductions. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen12.1 (   𝜑   ▶   𝜓   )
Assertion
Ref Expression
gen12 (   𝜑   ▶   𝑥𝑦𝜓   )
Distinct variable groups:   𝜑,𝑥   𝜑,𝑦
Allowed substitution hints:   𝜓(𝑥,𝑦)

Proof of Theorem gen12
StepHypRef Expression
1 gen12.1 . . . 4 (   𝜑   ▶   𝜓   )
21in1 39544 . . 3 (𝜑𝜓)
32alrimivv 2024 . 2 (𝜑 → ∀𝑥𝑦𝜓)
43dfvd1ir 39546 1 (   𝜑   ▶   𝑥𝑦𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wal 1651  (   wvd1 39542
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006
This theorem depends on definitions:  df-bi 199  df-vd1 39543
This theorem is referenced by:  sspwtr  39804  pwtrVD  39807  pwtrrVD  39808  suctrALT2VD  39819  truniALTVD  39861  trintALTVD  39863  suctrALTcfVD  39906
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