Theorem e20 45694

Description: A virtual deduction elimination rule (see syl6mpi 68). (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e20.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
e20.2	⊢ 𝜃
e20.3	⊢ (𝜒 → (𝜃 → 𝜏))

Assertion

Ref	Expression
e20	⊢ (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e20

Step	Hyp	Ref	Expression
1		e20.1	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2		e20.2	. . 3 ⊢ 𝜃
3	2	vd02 45566	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜃   )
4		e20.3	. 2 ⊢ (𝜒 → (𝜃 → 𝜏))
5	1, 3, 4	e22 45639	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜏   )

This proof depends on syntax axioms:   → wi 4  (   wvd2 45545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-vd2 45546

This theorem is used by:  e20an  45695  tratrbVD  45828  onfrALTlem3VD  45854