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

Metamath Proof Explorer

Theorem com24

Description: Commutation of antecedents. Swap 2nd and 4th. Deduction associated with com13 . (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)

		Ref	Expression
	Hypothesis	com4.1	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$
	Assertion	com24	$⊢ φ \to (θ \to (χ \to (ψ \to τ)))$

Proof

Step	Hyp	Ref	Expression
1		com4.1	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$
2	1	com4t	$⊢ χ \to (θ \to (φ \to (ψ \to τ)))$
3	2	com13	$⊢ φ \to (θ \to (χ \to (ψ \to τ)))$