Theorem e1bi

Description: Biconditional form of e1a . sylib is e1bi without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1bi.1	⊢ (    𝜑    ▶    𝜓    )
	e1bi.2	⊢ ( 𝜓 ↔ 𝜒 )
Assertion	e1bi	⊢ (    𝜑    ▶    𝜒    )

Proof

Step	Hyp	Ref	Expression
1		e1bi.1	⊢ (    𝜑    ▶    𝜓    )
2		e1bi.2	⊢ ( 𝜓 ↔ 𝜒 )
3	2	biimpi	⊢ ( 𝜓 → 𝜒 )
4	1 3	e1a	⊢ (    𝜑    ▶    𝜒    )