Theorem e02 42317

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e02.1	⊢ 𝜑
e02.2	⊢ (   𝜓   ,   𝜒   ▶   𝜃   )
e02.3	⊢ (𝜑 → (𝜃 → 𝜏))

Assertion

Ref	Expression
e02	⊢ (   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e02

Step	Hyp	Ref	Expression
1		e02.1	. . 3 ⊢ 𝜑
2	1	vd02 42218	. 2 ⊢ (   𝜓   ,   𝜒   ▶   𝜑   )
3		e02.2	. 2 ⊢ (   𝜓   ,   𝜒   ▶   𝜃   )
4		e02.3	. 2 ⊢ (𝜑 → (𝜃 → 𝜏))
5	2, 3, 4	e22 42291	1 ⊢ (   𝜓   ,   𝜒   ▶   𝜏   )

Syntax hints:   → wi 4  (   wvd2 42197

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-vd2 42198

This theorem is referenced by:  e02an  42318  onfrALTlem3VD  42507  vk15.4jVD  42534