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Metamath Proof Explorer

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