Theorem e002 42152

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

Hypotheses

Ref	Expression
e002.1	⊢ 𝜑
e002.2	⊢ 𝜓
e002.3	⊢ (   𝜒   ,   𝜃   ▶   𝜏   )
e002.4	⊢ (𝜑 → (𝜓 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
e002	⊢ (   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e002

Step	Hyp	Ref	Expression
1		e002.1	. . 3 ⊢ 𝜑
2	1	vd02 42107	. 2 ⊢ (   𝜒   ,   𝜃   ▶   𝜑   )
3		e002.2	. . 3 ⊢ 𝜓
4	3	vd02 42107	. 2 ⊢ (   𝜒   ,   𝜃   ▶   𝜓   )
5		e002.3	. 2 ⊢ (   𝜒   ,   𝜃   ▶   𝜏   )
6		e002.4	. 2 ⊢ (𝜑 → (𝜓 → (𝜏 → 𝜂)))
7	2, 4, 5, 6	e222 42145	1 ⊢ (   𝜒   ,   𝜃   ▶   𝜂   )

Syntax hints:   → wi 4  (   wvd2 42086

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 396  df-vd2 42087

This theorem is referenced by: (None)