Theorem e012 42240

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

Hypotheses

Ref	Expression
e012.1	⊢ 𝜑
e012.2	⊢ (   𝜓   ▶   𝜒   )
e012.3	⊢ (   𝜓   ,   𝜃   ▶   𝜏   )
e012.4	⊢ (𝜑 → (𝜒 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
e012	⊢ (   𝜓   ,   𝜃   ▶   𝜂   )

Proof of Theorem e012

Step	Hyp	Ref	Expression
1		e012.1	. . 3 ⊢ 𝜑
2	1	vd01 42170	. 2 ⊢ (   𝜓   ▶   𝜑   )
3		e012.2	. 2 ⊢ (   𝜓   ▶   𝜒   )
4		e012.3	. 2 ⊢ (   𝜓   ,   𝜃   ▶   𝜏   )
5		e012.4	. 2 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜂)))
6	2, 3, 4, 5	e112 42227	1 ⊢ (   𝜓   ,   𝜃   ▶   𝜂   )

Syntax hints:   → wi 4  (   wvd1 42142  (   wvd2 42150

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-vd1 42143  df-vd2 42151

This theorem is referenced by: (None)