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Theorem el0321old 39444
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el0321old.1 𝜑
el0321old.2 (   (   𝜓   ,   𝜒   ,   𝜃   )   ▶   𝜏   )
el0321old.3 ((𝜑𝜏) → 𝜂)
Assertion
Ref Expression
el0321old (   (   𝜓   ,   𝜒   ,   𝜃   )   ▶   𝜂   )

Proof of Theorem el0321old
StepHypRef Expression
1 el0321old.1 . . 3 𝜑
2 el0321old.2 . . . 4 (   (   𝜓   ,   𝜒   ,   𝜃   )   ▶   𝜏   )
32dfvd3ani 39313 . . 3 ((𝜓𝜒𝜃) → 𝜏)
4 el0321old.3 . . 3 ((𝜑𝜏) → 𝜂)
51, 3, 4eel0321old 39443 . 2 ((𝜓𝜒𝜃) → 𝜂)
65dfvd3anir 39314 1 (   (   𝜓   ,   𝜒   ,   𝜃   )   ▶   𝜂   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  (   wvd1 39287  (   wvhc3 39306 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 197  df-an 385  df-vd1 39288  df-vhc3 39307 This theorem is referenced by:  suctrALTcfVD  39658
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