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 )