Theorem el1 45596

Description: A Virtual deduction elimination rule. syl 18 is el1 45596 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
el1.1	⊢ (   𝜑   ▶   𝜓   )
el1.2	⊢ (𝜓 → 𝜒)

Assertion

Ref	Expression
el1	⊢ (   𝜑   ▶   𝜒   )

Proof of Theorem el1

Step	Hyp	Ref	Expression
1		el1.1	. . . 4 ⊢ (   𝜑   ▶   𝜓   )
2	1	in1 45539	. . 3 ⊢ (𝜑 → 𝜓)
3		el1.2	. . 3 ⊢ (𝜓 → 𝜒)
4	2, 3	syl 18	. 2 ⊢ (𝜑 → 𝜒)
5	4	dfvd1ir 45541	1 ⊢ (   𝜑   ▶   𝜒   )

This proof depends on syntax axioms:   → wi 4  (   wvd1 45537

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-vd1 45538

This theorem is used by:  sspwimpVD  45886  sspwimpcfVD  45888  suctrALTcfVD  45890