This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm5.74rd

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 19-Mar-1997)

		Ref	Expression
	Hypothesis	pm5.74rd.1	$⊢ φ \to ((ψ \to χ) \leftrightarrow (ψ \to θ))$
	Assertion	pm5.74rd	$⊢ φ \to (ψ \to (χ \leftrightarrow θ))$

Step	Hyp	Ref	Expression
1		pm5.74rd.1	$⊢ φ \to ((ψ \to χ) \leftrightarrow (ψ \to θ))$
2		pm5.74	$⊢ (ψ \to (χ \leftrightarrow θ)) \leftrightarrow ((ψ \to χ) \leftrightarrow (ψ \to θ))$
3	1 2	sylibr	$⊢ φ \to (ψ \to (χ \leftrightarrow θ))$