Metamath Proof Explorer


Theorem gen21

Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 is alrimdv with virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis gen21.1 (    𝜑    ,    𝜓    ▶    𝜒    )
Assertion gen21 (    𝜑    ,    𝜓    ▶   𝑥 𝜒    )

Proof

Step Hyp Ref Expression
1 gen21.1 (    𝜑    ,    𝜓    ▶    𝜒    )
2 1 dfvd2i ( 𝜑 → ( 𝜓𝜒 ) )
3 2 alrimdv ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) )
4 3 dfvd2ir (    𝜑    ,    𝜓    ▶   𝑥 𝜒    )