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Metamath Proof Explorer

Theorem e2bir

Description: Right biconditional form of e2 . imbitrrdi is e2bir without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2bir.1	$⊢ (φ, ψ \to χ)$
	e2bir.2	$⊢ θ \leftrightarrow χ$
Assertion	e2bir	$⊢ (φ, ψ \to θ)$

Proof

Step	Hyp	Ref	Expression
1		e2bir.1	$⊢ (φ, ψ \to χ)$
2		e2bir.2	$⊢ θ \leftrightarrow χ$
3	2	biimpri	$⊢ χ \to θ$
4	1 3	e2	$⊢ (φ, ψ \to θ)$