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Theorem gen21nv 39360
Description: Virtual deduction form of alrimdh 1951. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
gen21nv.1 (𝜑 → ∀𝑥𝜑)
gen21nv.2 (𝜓 → ∀𝑥𝜓)
gen21nv.3 (   𝜑   ,   𝜓   ▶   𝜒   )
Assertion
Ref Expression
gen21nv (   𝜑   ,   𝜓   ▶   𝑥𝜒   )

Proof of Theorem gen21nv
StepHypRef Expression
1 gen21nv.1 . . 3 (𝜑 → ∀𝑥𝜑)
2 gen21nv.2 . . 3 (𝜓 → ∀𝑥𝜓)
3 gen21nv.3 . . . 4 (   𝜑   ,   𝜓   ▶   𝜒   )
43dfvd2i 39316 . . 3 (𝜑 → (𝜓𝜒))
51, 2, 4alrimdh 1951 . 2 (𝜑 → (𝜓 → ∀𝑥𝜒))
65dfvd2ir 39317 1 (   𝜑   ,   𝜓   ▶   𝑥𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1635  (   wvd2 39308
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894
This theorem depends on definitions:  df-bi 198  df-an 385  df-vd2 39309
This theorem is referenced by:  ssralv2VD  39613
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