Theorem int2 42226

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 42226 is ex 413. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
int2.1	⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜒   )

Assertion

Ref	Expression
int2	⊢ (   𝜑   ▶   (𝜓 → 𝜒)   )

Proof of Theorem int2

Step	Hyp	Ref	Expression
1		int2.1	. . . 4 ⊢ (   (   𝜑   ,   𝜓   )   ▶   𝜒   )
2	1	dfvd2ani 42203	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
3	2	ex 413	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	3	dfvd1ir 42193	1 ⊢ (   𝜑   ▶   (𝜓 → 𝜒)   )

Syntax hints:   → wi 4  (   wvd1 42189  (   wvhc2 42200

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 397  df-vd1 42190  df-vhc2 42201

This theorem is referenced by:  sspwimpVD  42539  sspwimpcfVD  42541  suctrALTcfVD  42543