Theorem pm2.61dne

Description: Deduction eliminating an inequality in an antecedent. (Contributed by NM, 1-Jun-2007) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	pm2.61dne.1	$$⊢\phi \to \left(A=B\to \psi \right)$$
	pm2.61dne.2	$$⊢\phi \to \left(A\ne B\to \psi \right)$$
Assertion	pm2.61dne	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.61dne.1	$$⊢\phi \to \left(A=B\to \psi \right)$$
2		pm2.61dne.2	$$⊢\phi \to \left(A\ne B\to \psi \right)$$
3	1	com12	$$⊢A=B\to \left(\phi \to \psi \right)$$
4	2	com12	$$⊢A\ne B\to \left(\phi \to \psi \right)$$
5	3 4	pm2.61ine	$$⊢\phi \to \psi$$