Theorem coeq1i

Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000)

	Ref	Expression
Hypothesis	coeq1i.1	⊢ 𝐴 = 𝐵
Assertion	coeq1i	⊢ ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		coeq1i.1	⊢ 𝐴 = 𝐵
2		coeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐶 )