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Theorem gen11nv 39159
Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis without distinct variables. alrimih 1791 is gen11nv 39159 without virtual deductions. (Contributed by Alan Sare, 12-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
gen11nv.1 (𝜑 → ∀𝑥𝜑)
gen11nv.2 (   𝜑   ▶   𝜓   )
Assertion
Ref Expression
gen11nv (   𝜑   ▶   𝑥𝜓   )

Proof of Theorem gen11nv
StepHypRef Expression
1 gen11nv.1 . . 3 (𝜑 → ∀𝑥𝜑)
2 gen11nv.2 . . . 4 (   𝜑   ▶   𝜓   )
32in1 39104 . . 3 (𝜑𝜓)
41, 3alrimih 1791 . 2 (𝜑 → ∀𝑥𝜓)
54dfvd1ir 39106 1 (   𝜑   ▶   𝑥𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521  (   wvd1 39102
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-vd1 39103
This theorem is referenced by:  tratrbVD  39411  hbimpgVD  39454  hbalgVD  39455  hbexgVD  39456  e2ebindVD  39462
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