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	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	pm2.21ddne.2	⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )
Assertion	pm2.21ddne	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		pm2.21ddne.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		pm2.21ddne.2	⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )
3	2	neneqd	⊢ ( 𝜑 → ¬ 𝐴 = 𝐵 )
4	1 3	pm2.21dd	⊢ ( 𝜑 → 𝜓 )