Theorem e120 42172

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 10-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e120.1	⊢ (   𝜑   ▶   𝜓   )
e120.2	⊢ (   𝜑   ,   𝜒   ▶   𝜃   )
e120.3	⊢ 𝜏
e120.4	⊢ (𝜓 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
e120	⊢ (   𝜑   ,   𝜒   ▶   𝜂   )

Proof of Theorem e120

Step	Hyp	Ref	Expression
1		e120.1	. . 3 ⊢ (   𝜑   ▶   𝜓   )
2	1	vd12 42109	. 2 ⊢ (   𝜑   ,   𝜒   ▶   𝜓   )
3		e120.2	. 2 ⊢ (   𝜑   ,   𝜒   ▶   𝜃   )
4		e120.3	. 2 ⊢ 𝜏
5		e120.4	. 2 ⊢ (𝜓 → (𝜃 → (𝜏 → 𝜂)))
6	2, 3, 4, 5	e220 42146	1 ⊢ (   𝜑   ,   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:  pwtrrVD  42334