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Theorem el021old 39424
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el021old.1 𝜑
el021old.2 (   (   𝜓   ,   𝜒   )   ▶   𝜃   )
el021old.3 ((𝜑𝜃) → 𝜏)
Assertion
Ref Expression
el021old (   (   𝜓   ,   𝜒   )   ▶   𝜏   )

Proof of Theorem el021old
StepHypRef Expression
1 el021old.1 . . 3 𝜑
2 el021old.2 . . . 4 (   (   𝜓   ,   𝜒   )   ▶   𝜃   )
32dfvd2ani 39297 . . 3 ((𝜓𝜒) → 𝜃)
4 el021old.3 . . 3 ((𝜑𝜃) → 𝜏)
51, 3, 4sylancr 698 . 2 ((𝜓𝜒) → 𝜏)
65dfvd2anir 39298 1 (   (   𝜓   ,   𝜒   )   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  (   wvd1 39283  (   wvhc2 39294
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 39284  df-vhc2 39295
This theorem is referenced by:  sspwimpcfVD  39652  suctrALTcfVD  39654
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