Theorem e01 41045

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e01.1	⊢ 𝜑
e01.2	⊢ (   𝜓   ▶   𝜒   )
e01.3	⊢ (𝜑 → (𝜒 → 𝜃))

Assertion

Ref	Expression
e01	⊢ (   𝜓   ▶   𝜃   )

Proof of Theorem e01

Step	Hyp	Ref	Expression
1		e01.1	. . 3 ⊢ 𝜑
2	1	vd01 40951	. 2 ⊢ (   𝜓   ▶   𝜑   )
3		e01.2	. 2 ⊢ (   𝜓   ▶   𝜒   )
4		e01.3	. 2 ⊢ (𝜑 → (𝜒 → 𝜃))
5	2, 3, 4	e11 41042	1 ⊢ (   𝜓   ▶   𝜃   )

Syntax hints:   → wi 4  (   wvd1 40923

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 209  df-vd1 40924

This theorem is referenced by:  e01an  41046  trsspwALT  41172  sspwtr  41175  pwtrVD  41178  pwtrrVD  41179  snssiALTVD  41181  snelpwrVD  41185  sstrALT2VD  41188  suctrALT2VD  41190  3impexpVD  41210  ax6e2eqVD  41261  ax6e2ndVD  41262  2sb5ndVD  41264  vk15.4jVD  41268