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Metamath Proof Explorer

Theorem mp2d

Description: A double modus ponens deduction. Deduction associated with mp2 . (Contributed by NM, 23-May-2013) (Proof shortened by Wolf Lammen, 23-Jul-2013)

	Ref	Expression
Hypotheses	mp2d.1	$⊢ φ \to ψ$
	mp2d.2	$⊢ φ \to χ$
	mp2d.3	$⊢ φ \to (ψ \to (χ \to θ))$
Assertion	mp2d	$⊢ φ \to θ$

Proof

Step	Hyp	Ref	Expression
1		mp2d.1	$⊢ φ \to ψ$
2		mp2d.2	$⊢ φ \to χ$
3		mp2d.3	$⊢ φ \to (ψ \to (χ \to θ))$
4	2 3	mpid	$⊢ φ \to (ψ \to θ)$
5	1 4	mpd	$⊢ φ \to θ$