Theorem iden2 42234

Description: Virtual deduction identity rule. simpr 485 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

Step	Hyp	Ref	Expression
1		simpr 485	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2		dfvd2an 42202	. 2 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜓   ) ↔ ((𝜑 ∧ 𝜓) → 𝜓))
3	1, 2	mpbir 230	1 ⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜓   )

Syntax hints:   → wi 4   ∧ wa 396  (   wvd1 42189  (   wvhc2 42200

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 206  df-an 397  df-vd1 42190  df-vhc2 42201

This theorem is referenced by: (None)