Theorem e20 42236

Description: A virtual deduction elimination rule (see syl6mpi 67). (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 42107	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜃   )
4		e20.3	. 2 ⊢ (𝜒 → (𝜃 → 𝜏))
5	1, 3, 4	e22 42180	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜏   )

Syntax hints:   → wi 4  (   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-vd2 42087

This theorem is referenced by:  e20an  42237  tratrbVD  42370  onfrALTlem3VD  42396