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Metamath Proof Explorer

Theorem com23

Description: Commutation of antecedents. Swap 2nd and 3rd. Deduction associated with com12 . (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 4-Aug-2012)

		Ref	Expression
	Hypothesis	com3.1	$⊢ φ \to (ψ \to (χ \to θ))$
	Assertion	com23	$⊢ φ \to (χ \to (ψ \to θ))$

Proof

Step	Hyp	Ref	Expression
1		com3.1	$⊢ φ \to (ψ \to (χ \to θ))$
2		pm2.27	$⊢ χ \to ((χ \to θ) \to θ)$
3	1 2	syl9	$⊢ φ \to (χ \to (ψ \to θ))$