Theorem e021 42174

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

Hypotheses

Ref	Expression
e021.1	⊢ 𝜑
e021.2	⊢ (   𝜓   ,   𝜒   ▶   𝜃   )
e021.3	⊢ (   𝜓   ▶   𝜏   )
e021.4	⊢ (𝜑 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
e021	⊢ (   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e021

Step	Hyp	Ref	Expression
1		e021.1	. . 3 ⊢ 𝜑
2	1	vd01 42106	. 2 ⊢ (   𝜓   ▶   𝜑   )
3		e021.2	. 2 ⊢ (   𝜓   ,   𝜒   ▶   𝜃   )
4		e021.3	. 2 ⊢ (   𝜓   ▶   𝜏   )
5		e021.4	. 2 ⊢ (𝜑 → (𝜃 → (𝜏 → 𝜂)))
6	2, 3, 4, 5	e121 42165	1 ⊢ (   𝜓   ,   𝜒   ▶   𝜂   )

Syntax hints:   → wi 4  (   wvd1 42078  (   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-vd1 42079  df-vd2 42087

This theorem is referenced by: (None)