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 )