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Theorem el1 39353
Description: A Virtual deduction elimination rule. syl 17 is el1 39353 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el1.1 (   𝜑   ▶   𝜓   )
el1.2 (𝜓𝜒)
Assertion
Ref Expression
el1 (   𝜑   ▶   𝜒   )

Proof of Theorem el1
StepHypRef Expression
1 el1.1 . . . 4 (   𝜑   ▶   𝜓   )
21in1 39287 . . 3 (𝜑𝜓)
3 el1.2 . . 3 (𝜓𝜒)
42, 3syl 17 . 2 (𝜑𝜒)
54dfvd1ir 39289 1 (   𝜑   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39285
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-vd1 39286
This theorem is referenced by:  sspwimpVD  39652  sspwimpcfVD  39654  suctrALTcfVD  39656
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