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Metamath Proof Explorer

Theorem ee3bir

Description: Right-biconditional form of e3 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 22-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee3bir.1	$⊢ φ \to (ψ \to (χ \to θ))$
	ee3bir.2	$⊢ τ \leftrightarrow θ$
Assertion	ee3bir	$⊢ φ \to (ψ \to (χ \to τ))$

Proof

Step	Hyp	Ref	Expression
1		ee3bir.1	$⊢ φ \to (ψ \to (χ \to θ))$
2		ee3bir.2	$⊢ τ \leftrightarrow θ$
3	2	biimpri	$⊢ θ \to τ$
4	1 3	syl8	$⊢ φ \to (ψ \to (χ \to τ))$