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Metamath Proof Explorer

Theorem neqcomd

Description: Commute an inequality. (Contributed by Rohan Ridenour, 3-Aug-2023)

Ref Expression
Hypothesis neqcomd.1 ⊢ φ → ¬ A = B
Assertion neqcomd ⊢ φ → ¬ B = A

Proof

Step Hyp Ref Expression
1 neqcomd.1 ⊢ φ → ¬ A = B
2 eqcom ⊢ A = B ↔ B = A
3 1 2 sylnib ⊢ φ → ¬ B = A