Theorem e3bi

Description: Biconditional form of e3 . syl8ib is e3bi without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e3bi.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e3bi.2	⊢ ( 𝜃 ↔ 𝜏 )
Assertion	e3bi	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e3bi.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e3bi.2	⊢ ( 𝜃 ↔ 𝜏 )
3	2	biimpi	⊢ ( 𝜃 → 𝜏 )
4	1 3	e3	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )