Theorem dfvd2an 40909

Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dfvd2an	⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))

Proof of Theorem dfvd2an

Step	Hyp	Ref	Expression
1		df-vd1 40897	. 2 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((   𝜑   ,   𝜓   ) → 𝜒))
2		df-vhc2 40908	. . 3 ⊢ ((   𝜑   ,   𝜓   ) ↔ (𝜑 ∧ 𝜓))
3	2	imbi1i 352	. 2 ⊢ (((   𝜑   ,   𝜓   ) → 𝜒) ↔ ((𝜑 ∧ 𝜓) → 𝜒))
4	1, 3	bitri 277	1 ⊢ ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑 ∧ 𝜓) → 𝜒))

Syntax hints:   → wi 4   ↔ wb 208   ∧ wa 398  (   wvd1 40896  (   wvhc2 40907

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 209  df-vd1 40897  df-vhc2 40908

This theorem is referenced by:  dfvd2ani  40910  dfvd2anir  40911  iden2  40941