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    )