Theorem e3 42310

Description: Meta-connective form of syl8 76. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e3.1	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e3.2	⊢ (𝜃 → 𝜏)

Assertion

Ref	Expression
e3	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e3

Step	Hyp	Ref	Expression
1		e3.1	. 2 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2		e3.2	. . 3 ⊢ (𝜃 → 𝜏)
3	2	a1i 11	. 2 ⊢ (𝜃 → (𝜃 → 𝜏))
4	1, 1, 3	e33 42307	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Syntax hints:   → wi 4  (   wvd3 42160

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 42163

This theorem is referenced by:  e3bi  42311  e3bir  42312  truniALTVD  42451  onfrALTlem2VD  42462