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Metamath Proof Explorer

Theorem e3

Description: Meta-connective form of syl8 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e3.1 ⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
e3.2 ⊢ ( 𝜃 → 𝜏 )
Assertion e3 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e3.1 ⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2 e3.2 ⊢ ( 𝜃 → 𝜏 )
3 2 a1i ⊢ ( 𝜃 → ( 𝜃 → 𝜏 ) )
4 1 1 3 e33 ⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )