Theorem rmyneg

Description: Negation formula for Y sequence (odd function). (Contributed by Stefan O'Rear, 22-Sep-2014)

	Ref	Expression
Assertion	rmyneg	⊢ ( ( 𝐴 ∈ ( ℤ≥ ‘ 2 ) ∧ 𝑁 ∈ ℤ ) → ( 𝐴 Yrm - 𝑁 ) = - ( 𝐴 Yrm 𝑁 ) )

Proof

Step	Hyp	Ref	Expression
1		rmxyneg	⊢ ( ( 𝐴 ∈ ( ℤ≥ ‘ 2 ) ∧ 𝑁 ∈ ℤ ) → ( ( 𝐴 Xrm - 𝑁 ) = ( 𝐴 Xrm 𝑁 ) ∧ ( 𝐴 Yrm - 𝑁 ) = - ( 𝐴 Yrm 𝑁 ) ) )
2	1	simprd	⊢ ( ( 𝐴 ∈ ( ℤ≥ ‘ 2 ) ∧ 𝑁 ∈ ℤ ) → ( 𝐴 Yrm - 𝑁 ) = - ( 𝐴 Yrm 𝑁 ) )