Theorem pm2.21ddne

Description: A contradiction implies anything. Equality/inequality deduction form. (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypotheses	pm2.21ddne.1	|- ( ph -> A = B )
	pm2.21ddne.2	|- ( ph -> A =/= B )
Assertion	pm2.21ddne	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		pm2.21ddne.1	|- ( ph -> A = B )
2		pm2.21ddne.2	|- ( ph -> A =/= B )
3	2	neneqd	|- ( ph -> -. A = B )
4	1 3	pm2.21dd	|- ( ph -> ps )