Theorem int3 37858

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 37858 is 3expia 1259. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
int3.1	⊢ (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )

Assertion

Ref	Expression
int3	⊢ (   (   𝜑   ,   𝜓   )   ▶   (𝜒 → 𝜃)   )

Proof of Theorem int3

Step	Hyp	Ref	Expression
1		int3.1	. . . 4 ⊢ (   (   𝜑   ,   𝜓   ,   𝜒   )   ▶   𝜃   )
2	1	dfvd3ani 37832	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
3	2	3expia 1259	. 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃))
4	3	dfvd2anir 37821	1 ⊢ (   (   𝜑   ,   𝜓   )   ▶   (𝜒 → 𝜃)   )

Syntax hints:   → wi 4  (   wvd1 37806  (   wvhc2 37817  (   wvhc3 37825

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 196  df-an 385  df-3an 1033  df-vd1 37807  df-vhc2 37818  df-vhc3 37826

This theorem is referenced by:  suctrALTcfVD  38181