Theorem imsym1

Description: A symmetry with -> .

See negsym1 for more information. (Contributed by Anthony Hart, 4-Sep-2011)

	Ref	Expression
Assertion	imsym1	$$⊢\left(\psi \to \left(\psi \to \perp \right)\right)\to \left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \psi \to \left(\psi \to \phi \right)$$
2		falim	$$⊢\perp \to \phi$$
3	2	imim2i	$$⊢\left(\psi \to \perp \right)\to \left(\psi \to \phi \right)$$
4	1 3	ja	$$⊢\left(\psi \to \left(\psi \to \perp \right)\right)\to \left(\psi \to \phi \right)$$