Metamath Proof Explorer


Theorem el1

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

Ref Expression
Hypotheses el1.1 (    𝜑    ▶    𝜓    )
el1.2 ( 𝜓𝜒 )
Assertion el1 (    𝜑    ▶    𝜒    )

Proof

Step Hyp Ref Expression
1 el1.1 (    𝜑    ▶    𝜓    )
2 el1.2 ( 𝜓𝜒 )
3 1 in1 ( 𝜑𝜓 )
4 3 2 syl ( 𝜑𝜒 )
5 4 dfvd1ir (    𝜑    ▶    𝜒    )