Theorem vd02 45421

Description: Two virtual hypotheses virtually infer a theorem. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
vd02.1	⊢ 𝜑

Assertion

Ref	Expression
vd02	⊢ (   𝜓   ,   𝜒   ▶   𝜑   )

Proof of Theorem vd02

Step	Hyp	Ref	Expression
1		vd02.1	. . . 4 ⊢ 𝜑
2	1	a1i 11	. . 3 ⊢ (𝜒 → 𝜑)
3	2	a1i 11	. 2 ⊢ (𝜓 → (𝜒 → 𝜑))
4	3	dfvd2ir 45409	1 ⊢ (   𝜓   ,   𝜒   ▶   𝜑   )

This proof depends on syntax axioms:   → wi 4  (   wvd2 45400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-vd2 45401

This theorem is used by:  e220  45460  e202  45462  e022  45464  e002  45466  e020  45468  e200  45470  e02  45520  e20  45549