Theorem vd02 42107

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 42095	1 ⊢ (   𝜓   ,   𝜒   ▶   𝜑   )

Syntax hints:   → wi 4  (   wvd2 42086

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-vd2 42087

This theorem is referenced by:  e220  42146  e202  42148  e022  42150  e002  42152  e020  42154  e200  42156  e02  42206  e20  42236