Theorem e03 42360

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e03.1	⊢ 𝜑
e03.2	⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
e03.3	⊢ (𝜑 → (𝜏 → 𝜂))

Assertion

Ref	Expression
e03	⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e03

Step	Hyp	Ref	Expression
1		e03.1	. . 3 ⊢ 𝜑
2	1	vd03 42219	. 2 ⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜑   )
3		e03.2	. 2 ⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
4		e03.3	. 2 ⊢ (𝜑 → (𝜏 → 𝜂))
5	2, 3, 4	e33 42354	1 ⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )

Syntax hints:   → wi 4  (   wvd3 42207

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 397  df-3an 1088  df-vd3 42210

This theorem is referenced by:  e03an  42362  suctrALT2VD  42456