Metamath Proof Explorer


Theorem e12

Description: A virtual deduction elimination rule (see sylsyld ). (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e12.1 (    𝜑    ▶    𝜓    )
e12.2 (    𝜑    ,    𝜒    ▶    𝜃    )
e12.3 ( 𝜓 → ( 𝜃𝜏 ) )
Assertion e12 (    𝜑    ,    𝜒    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e12.1 (    𝜑    ▶    𝜓    )
2 e12.2 (    𝜑    ,    𝜒    ▶    𝜃    )
3 e12.3 ( 𝜓 → ( 𝜃𝜏 ) )
4 1 vd12 (    𝜑    ,    𝜒    ▶    𝜓    )
5 4 2 3 e22 (    𝜑    ,    𝜒    ▶    𝜏    )