Theorem el1 40960

Description: A Virtual deduction elimination rule. syl 17 is el1 40960 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 40903	. . 3 ⊢ (𝜑 → 𝜓)
3		el1.2	. . 3 ⊢ (𝜓 → 𝜒)
4	2, 3	syl 17	. 2 ⊢ (𝜑 → 𝜒)
5	4	dfvd1ir 40905	1 ⊢ (   𝜑   ▶   𝜒   )

Syntax hints:   → wi 4  (   wvd1 40901

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 209  df-vd1 40902

This theorem is referenced by:  sspwimpVD  41251  sspwimpcfVD  41253  suctrALTcfVD  41255