Theorem e33 42243

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

Hypotheses

Ref	Expression
e33.1	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e33.2	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
e33.3	⊢ (𝜃 → (𝜏 → 𝜂))

Assertion

Ref	Expression
e33	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e33

Step	Hyp	Ref	Expression
1		e33.1	. 2 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2		e33.2	. 2 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
3		e33.3	. . 3 ⊢ (𝜃 → (𝜏 → 𝜂))
4	3	a1i 11	. 2 ⊢ (𝜃 → (𝜃 → (𝜏 → 𝜂)))
5	1, 1, 2, 4	e333 42242	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Syntax hints:   → wi 4  (   wvd3 42096

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-3an 1087  df-vd3 42099

This theorem is referenced by:  e33an  42244  e3  42246  e03  42249  e30  42253  e13  42257  e31  42260  e23  42264  e32  42267  truniALTVD  42387  trintALTVD  42389  onfrALTlem2VD  42398