Theorem coeq1d

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

	Ref	Expression
Hypothesis	coeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	coeq1d	⊢ ( 𝜑 → ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		coeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		coeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐶 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ∘ 𝐶 ) = ( 𝐵 ∘ 𝐶 ) )