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Metamath Proof Explorer

Theorem necomd

Description: Deduction from commutative law for inequality. (Contributed by NM, 12-Feb-2008)

Ref Expression
Hypothesis necomd.1 ⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )
Assertion necomd ( 𝜑 → 𝐵 ≠ 𝐴 )

Proof

Step Hyp Ref Expression
1 necomd.1 ⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )
2 necom ⊢ ( 𝐴 ≠ 𝐵 ↔ 𝐵 ≠ 𝐴 )
3 1 2 sylib ⊢ ( 𝜑 → 𝐵 ≠ 𝐴 )