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Metamath Proof Explorer

Theorem e3bir

Description: Right biconditional form of e3 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e3bir.1	$⊢ (φ, ψ, χ \to θ)$
	e3bir.2	$⊢ τ \leftrightarrow θ$
Assertion	e3bir	$⊢ (φ, ψ, χ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		e3bir.1	$⊢ (φ, ψ, χ \to θ)$
2		e3bir.2	$⊢ τ \leftrightarrow θ$
3	2	biimpri	$⊢ θ \to τ$
4	1 3	e3	$⊢ (φ, ψ, χ \to τ)$