Metamath Proof Explorer


Theorem e33

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e33.1 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
e33.2 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
e33.3 ( 𝜃 → ( 𝜏𝜂 ) )
Assertion e33 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e33.1 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2 e33.2 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
3 e33.3 ( 𝜃 → ( 𝜏𝜂 ) )
4 3 a1i ( 𝜃 → ( 𝜃 → ( 𝜏𝜂 ) ) )
5 1 1 2 4 e333 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )