Theorem vd03 42219

Description: A theorem is virtually inferred by the 3 virtual hypotheses. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
vd03.1	⊢ 𝜑

Assertion

Ref	Expression
vd03	⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜑   )

Proof of Theorem vd03

Step	Hyp	Ref	Expression
1		vd03.1	. . . . 5 ⊢ 𝜑
2	1	a1i 11	. . . 4 ⊢ (𝜃 → 𝜑)
3	2	a1i 11	. . 3 ⊢ (𝜒 → (𝜃 → 𝜑))
4	3	a1i 11	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜑)))
5	4	dfvd3ir 42213	1 ⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜑   )

Syntax hints:   → wi 4  (   wvd3 42207

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-3an 1088  df-vd3 42210

This theorem is referenced by:  e03  42360  e30  42364