This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem e2

Description: A virtual deduction elimination rule. syl6 is e2 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e2.1 ⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
e2.2 ⊢ ( 𝜒 → 𝜃 )
Assertion e2 (    𝜑    ,    𝜓    ▶    𝜃    )

Proof

Step Hyp Ref Expression
1 e2.1 ⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2 e2.2 ⊢ ( 𝜒 → 𝜃 )
3 1 dfvd2i ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4 3 2 syl6 ⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
5 4 dfvd2ir ⊢ (    𝜑    ,    𝜓    ▶    𝜃    )