Theorem e101 42187

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

Hypotheses

Ref	Expression
e101.1	⊢ (   𝜑   ▶   𝜓   )
e101.2	⊢ 𝜒
e101.3	⊢ (   𝜑   ▶   𝜃   )
e101.4	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
e101	⊢ (   𝜑   ▶   𝜏   )

Proof of Theorem e101

Step	Hyp	Ref	Expression
1		e101.1	. 2 ⊢ (   𝜑   ▶   𝜓   )
2		e101.2	. . 3 ⊢ 𝜒
3	2	vd01 42106	. 2 ⊢ (   𝜑   ▶   𝜒   )
4		e101.3	. 2 ⊢ (   𝜑   ▶   𝜃   )
5		e101.4	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
6	1, 3, 4, 5	e111 42183	1 ⊢ (   𝜑   ▶   𝜏   )

Syntax hints:   → wi 4  (   wvd1 42078

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-vd1 42079

This theorem is referenced by:  sbcoreleleqVD  42368