Theorem e010 42166

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

Hypotheses

Ref	Expression
e010.1	⊢ 𝜑
e010.2	⊢ (   𝜓   ▶   𝜒   )
e010.3	⊢ 𝜃
e010.4	⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
e010	⊢ (   𝜓   ▶   𝜏   )

Proof of Theorem e010

Step	Hyp	Ref	Expression
1		e010.1	. . 3 ⊢ 𝜑
2	1	vd01 42079	. 2 ⊢ (   𝜓   ▶   𝜑   )
3		e010.2	. 2 ⊢ (   𝜓   ▶   𝜒   )
4		e010.3	. . 3 ⊢ 𝜃
5	4	vd01 42079	. 2 ⊢ (   𝜓   ▶   𝜃   )
6		e010.4	. 2 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))
7	2, 3, 5, 6	e111 42156	1 ⊢ (   𝜓   ▶   𝜏   )

Syntax hints:   → wi 4  (   wvd1 42051

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 210  df-vd1 42052

This theorem is referenced by: (None)