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Metamath Proof Explorer

Theorem bi23imp13

Description: 3imp with middle implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017)

		Ref	Expression
	Hypothesis	bi23imp13.1	$⊢ φ \to (ψ \leftrightarrow (χ \to θ))$
	Assertion	bi23imp13	$⊢ (φ \land ψ \land χ) \to θ$

Step	Hyp	Ref	Expression
1		bi23imp13.1	$⊢ φ \to (ψ \leftrightarrow (χ \to θ))$
2	1	biimpd	$⊢ φ \to (ψ \to (χ \to θ))$
3	2	3imp	$⊢ (φ \land ψ \land χ) \to θ$