Theorem coideq

Description: Equality theorem for composition of two classes. (Contributed by Peter Mazsa, 23-Sep-2021)

	Ref	Expression
Assertion	coideq	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∘ 𝐴 ) = ( 𝐵 ∘ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		coeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∘ 𝐴 ) = ( 𝐵 ∘ 𝐴 ) )
2		coeq2	⊢ ( 𝐴 = 𝐵 → ( 𝐵 ∘ 𝐴 ) = ( 𝐵 ∘ 𝐵 ) )
3	1 2	eqtrd	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∘ 𝐴 ) = ( 𝐵 ∘ 𝐵 ) )