Theorem e201 45398

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

Hypotheses

Ref	Expression
e201.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
e201.2	⊢ 𝜃
e201.3	⊢ (   𝜑   ▶   𝜏   )
e201.4	⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
e201	⊢ (   𝜑   ,   𝜓   ▶   𝜂   )

Proof of Theorem e201

Step	Hyp	Ref	Expression
1		e201.1	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2		e201.2	. . 3 ⊢ 𝜃
3	2	vd01 45334	. 2 ⊢ (   𝜑   ▶   𝜃   )
4		e201.3	. 2 ⊢ (   𝜑   ▶   𝜏   )
5		e201.4	. 2 ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))
6	1, 3, 4, 5	e211 45394	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜂   )

This proof depends on syntax axioms:   → wi 4  (   wvd1 45306  (   wvd2 45314

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-vd1 45307  df-vd2 45315

This theorem is used by: (None)