Theorem e001 42195

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e001.1	⊢ 𝜑
e001.2	⊢ 𝜓
e001.3	⊢ (   𝜒   ▶   𝜃   )
e001.4	⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
e001	⊢ (   𝜒   ▶   𝜏   )

Proof of Theorem e001

Step	Hyp	Ref	Expression
1		e001.1	. . 3 ⊢ 𝜑
2	1	vd01 42106	. 2 ⊢ (   𝜒   ▶   𝜑   )
3		e001.2	. . 3 ⊢ 𝜓
4	3	vd01 42106	. 2 ⊢ (   𝜒   ▶   𝜓   )
5		e001.3	. 2 ⊢ (   𝜒   ▶   𝜃   )
6		e001.4	. 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏)))
7	2, 4, 5, 6	e111 42183	1 ⊢ (   𝜒   ▶   𝜏   )

Syntax hints:   → wi 4  (   wvd1 42078

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-vd1 42079

This theorem is referenced by: (None)