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Theorem gen31 41247
Description: Virtual deduction generalizing rule for one quantifying variable and three virtual hypothesis. gen31 41247 is ggen31 41171 with virtual deductions. (Contributed by Alan Sare, 22-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen31.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
Assertion
Ref Expression
gen31 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝑥𝜃   )
Distinct variable groups:   𝜒,𝑥   𝜑,𝑥   𝜓,𝑥
Allowed substitution hint:   𝜃(𝑥)

Proof of Theorem gen31
StepHypRef Expression
1 gen31.1 . . . 4 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
21dfvd3i 41218 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
32ggen31 41171 . 2 (𝜑 → (𝜓 → (𝜒 → ∀𝑥𝜃)))
43dfvd3ir 41219 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝑥𝜃   )
Colors of variables: wff setvar class
Syntax hints:  wal 1536  (   wvd3 41213
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912
This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086  df-vd3 41216
This theorem is referenced by:  onfrALTlem2VD  41515
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