Theorem pm2.86d

Description: Deduction associated with pm2.86 . (Contributed by NM, 29-Jun-1995) (Proof shortened by Wolf Lammen, 3-Apr-2013)

	Ref	Expression
Hypothesis	pm2.86d.1	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)\right)$$
Assertion	pm2.86d	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.86d.1	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)\right)$$
2		ax-1	$$⊢\chi \to \left(\psi \to \chi \right)$$
3	2 1	syl5	$$⊢\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)$$
4	3	com23	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$