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Theorem iden2 39333
Description: Virtual deduction identity rule. simpr 479 in conjunction form Virtual Deduction notation. (Contributed by Alan Sare, 5-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
iden2 (   (   𝜑   ,   𝜓   )   ▶   𝜓   )

Proof of Theorem iden2
StepHypRef Expression
1 simpr 479 . 2 ((𝜑𝜓) → 𝜓)
2 dfvd2an 39292 . 2 ((   (   𝜑   ,   𝜓   )   ▶   𝜓   ) ↔ ((𝜑𝜓) → 𝜓))
31, 2mpbir 221 1 (   (   𝜑   ,   𝜓   )   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  (   wvd1 39279  (   wvhc2 39290
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 39280  df-vhc2 39291
This theorem is referenced by: (None)
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