Theorem bcxmaslem1

Description: Lemma for bcxmas . (Contributed by Paul Chapman, 18-May-2007)

	Ref	Expression
Assertion	bcxmaslem1	⊢ ( 𝐴 = 𝐵 → ( ( 𝑁 + 𝐴 ) C 𝐴 ) = ( ( 𝑁 + 𝐵 ) C 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		oveq2	⊢ ( 𝐴 = 𝐵 → ( 𝑁 + 𝐴 ) = ( 𝑁 + 𝐵 ) )
2		id	⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 )
3	1 2	oveq12d	⊢ ( 𝐴 = 𝐵 → ( ( 𝑁 + 𝐴 ) C 𝐴 ) = ( ( 𝑁 + 𝐵 ) C 𝐵 ) )