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Metamath Proof Explorer

Theorem e2bi

Description: Biconditional form of e2 . imbitrdi is e2bi without virtual deductions. (Contributed by Alan Sare, 10-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2bi.1	$⊢ (φ, ψ \to χ)$
	e2bi.2	$⊢ χ \leftrightarrow θ$
Assertion	e2bi	$⊢ (φ, ψ \to θ)$

Proof

Step	Hyp	Ref	Expression
1		e2bi.1	$⊢ (φ, ψ \to χ)$
2		e2bi.2	$⊢ χ \leftrightarrow θ$
3	2	biimpi	$⊢ χ \to θ$
4	1 3	e2	$⊢ (φ, ψ \to θ)$